This question is different from: Do Calvinists believe that it is possible to be saved without believing the doctrine of predestination?
One asks "Does A => B?" the other asks "Does B => A" ?
Revelation 22:18–19 (KJV)
18 For I testify unto every man that heareth the words of the prophecy of this book, If any man shall add unto these things, God shall add unto him the plagues that are written in this book: 19 And if any man shall take away from the words of the book of this prophecy, God shall take away his part out of the book of life, and out of the holy city, and from the things which are written in this book.
I'm very hesitant to argue about salvation apart from "believing in Jesus"
Now, intuitively, it seems to me that it's very hard to believe in the doctrine of election without believing in Jesus. However,
James 2:18–19 (KJV)
18 Yea, a man may say, Thou hast faith, and I have works: shew me thy faith without thy works, and I will shew thee my faith by my works. 19 Thou believest that there is one God; thou doest well: the devils also believe, and tremble.
In this sense, even demons intellectually believe in the doctrine of predestination, yet it does them no good – thus perhaps there is the possibility that humans can intellectually believe in the doctrine of predestination, yet somehow not believe in Christ.
Anyway – these are my conflicted thoughts. Insights?