Yes, people can "verify His love by reading the Bible and studying His personality using basic logic (implications and equivalences)?" as you ask. Untold numbers of people these past 2,000 years, who have experienced the love of God, can find confirmation of that love when reading the Bible and learning more about the Being of God. Yet whether you, personally, can do that or not would depend on whether you have put your faith (trust) in God, irrespective of your personal feelings. There are plenty of people around (non-Christians included) who have great emotional surges of love towards God when they think they have had some personal encounter with God, yet for as long as they place their beliefs about God and his personality on their emotions, they will never understand the constancy of God's love in face of their inconsistent feelings and thoughts.
A key word in this question is "verify". To verify something is to first have had knowledge and evidence of the matter where verification is sought. Many people have knowledge of God in their lives, yet if that is merely a head-trip - theological knowledge - they could disbelieve the love of God to be consistent, especially if they think the righteous judgments of God are not righteous (according to their idea of logic). Such a view tends towards judging God, not seeking to "let God be found true, though every man a liar" (Romans 3:4). Note that a Psalm is then quoted: "as it is written, 'That thou might be justified in thy sayings, and might overcome when thou art judged'." (Psalm 51:4) That was king David confessing directly to God for being presumptuous in having held back for about a year before confessing his sin in the Bathsheba affair, after Nathan the prophet confronted him. David then acknowledged that God was justified in what he said, and righteous in his judgments.
Until that is the basis upon which we approach God, we will keep swithering between emotional feelings of love for him, and doubts about whether God is just and righteous. It is supremely in the cross of Christ that we see God's justice and righteous judgment against sin poured out, to be satisfied once and for all. Once we have grasped that, then we will see God very differently to those who think that "God is love" and nothing more.
Many people have evidence of God in their lives, yet they still think there is a capricious aspect to God. Being in turmoil about this, they try to blot out disturbing matters and focus, instead, on that which pleases them - feelings of love and positive answers to prayer etc. If they mix in circles where great emphasis is laid on supernatural experience attributed to the Holy Spirit, they may find their study of God's declared word to us being either shoved to the side or rationalized away to accommodate an over-emphasis on the Holy Spirit. Anyone wishing to honestly appraise this should read the book "Strange Fire?" by Eric. E. Wright, Evangelical Press, 1996.
The basic logic of God's love and his righteousness is wonderfully seen by learning from the written word of God what the Word of God achieved in his finished work on the cross. Never was such love demonstrated! Never was such righteousness worked out! Yet the world could not see nor understand.
"For God so loved the world that he gave his only-begotten Son, that whosoever believeth in him should not perish, but have eternal life." John 3:16
"In this was manifested the love of God toward us, because that God sent his only begotten Son into the world, that we might live through him. Herein is love, not that we loved God, but that he loved us, and sent his Son, the appeasement for our sins... We love him because he first loved us." 1 John 4:10-19
The logic lies in God taking the initiative to redeem repentant sinners, by sending his Son into this world. This Son is "the express image of [God's] person (Hebrews 1:3) so that Jesus could say to his disciples, "He that hath seen me hath seen the Father" (John 14:9). But now that Christ has returned to heaven, how are we to "see" him? By the words of scripture, that's how. There we learn of all the initiatives God has taken throughout the centuries to save his people and to judge unrepentant sinners. God's immense patience and forgiveness is shown, but also that he will not be mocked. Then, when we read of the Word of God becoming flesh (John ch. 1) and dwelling among people as man, we read further of his great love, patience, and utter goodness (even though he spoke in judgment against those who hated him.)
Tragically, many false prophets and false 'christs' have gone into the world, as Jesus warned would happen, and have deceived many. That is why sticking to what the scriptures say about God and Christ is imperative. All false religions either try to lower Christ a degree or two, or try to amalgamate their idea of 'christ' into existing pagan and superstitious beliefs. They will not give the glory due to heaven's beloved one. Yet he told us (in scripture, John 5:22-23) that the Father has committed all judgment to himself, the Son, "that all men should honour the Son, even as they honour the Father."
Those who disbelieve what the scriptures tell us about Christ are believing in a false 'christ', a man-made version. It is only by approaching in faith the Christ of scripture that we logically grasp the verification of the claim that God is love, and God is also holy and righteous.
Let Jesus have the last word here. He commanded religious people in his day to:
"Search the scriptures; for in them ye think ye have eternal life: and they are they which testify of me. And ye will not come to me, that ye might have life." John 5:39.
That is the tragedy of those who search the scriptures without first having come in faith to the Christ of those scriptures. Nobody who understands the love of God through experience and logic can do so without approaching the Father via the Christ. "No man can come to me, except the Father which hath sent me draw him..." John 6:44 and now John 14:6 where Jesus said, "I am the way, the truth, and the life: no man cometh unto the Father, but by me." Not a contradiction, nor even a paradox - the truth of how to know the Father is to know the Christ of scripture and to come to him, as the scriptures show. But come to an unscriptural 'christ', and you will always have doubts and think the ways of God are illogical.
As for Romans 11:33, that shows that we cannot plumb the depths of God's wisdom, knowledge, judgments and paths. That should never be used as as an excuse for not trying, as the Holy Spirit will open up our hearts and minds to this awesome God as we strive to search the scriptures sincerely.