Yes, I think it was a "belief unto salvation" and I think there is both a Biblical and logical argument to back that up.
Looking at the Strong's words for this chapter, this particular word, pisteuw, means:
believe, commit unto
The root word, pistiv, is even more explicit:
conviction of the truth of anything, belief; in the NT of a
conviction or belief respecting man's relationship to God and
divine things, generally with the included idea of trust and
holy fervour born of faith and joined with it
relating to God
the conviction that God exists and is the creator and
ruler of all things, the provider and bestower of eternal
salvation through Christ
and so on (see links for full details).
What else could "believe in Him" mean in this context? He had just said (v12):
"I am the light of the world. Whoever follows me will not walk in darkness, but will have the light of life."
"I told you that you would die in your sins, for unless you believe that I am he you will die in your sins."
So I cannot think of any other interpretation.
However, there is in addition a third reason:
Purpose of John's Gospel
Let's remember why John wrote his Gospel, explained in John 20:30-31:
Now Jesus did many other signs in the presence of the disciples, which are not written in this book; but these are written so that you may believe that Jesus is the Christ, the Son of God, and that by believing you may have life in his name.
Since John wanted people to believe (or go on believing) in Jesus, it makes sense that this story backs up that purpose.