In this case, it's a copout.
It's the equivalent of saying "I don't know if Jesus is Sovereign King or just a bystander.
I think most people understood my original statement. You can't seem to understand and I know you hate it when I bring in other sources but let me try once more.
"And as Moses lifted up the serpent in the wilderness, even so must the Son of Man be lifted up: That whosoever believeth in Him should not perish but have eternal life. Jesus
"For God so loved the world that He gave his only begotten son that whosoever believeth in Him should not perish but have everlasting life". Jesus
"He that believeth on Him is not condemned, but he that believeth not is condemned already because he has not believed in the name of the only begotten Son of God." Jesus
So the question comes up, why did some not believe?
"And this is the condemnation, that light is come into the world, and some were not chosen". Dave That's not what it says is it?
"And this is the condemnation, that light is come into the world, and men loved darkness rather than light, because their deeds were evil". Jesus
Let's get another opinion.
"He that believeth on the Son hath everlasting life, but he that believeth not the Son shall not see life; but the wrath of God abideth on him." John the Baptist
So the answer is, it ALL depends on whether a person believes or not. Or else Jesus and John were wrong. I have a developed theology and an opinion as to how this comes about and that theology puts a high value on the work of the Holy Spirit and has a low view of man's natural spiritual ability. Most people on here get that and some even respect where I'm coming from even if they don't agree. But I also respect the fact that those verses above, directly from our Lord, put a high premium on belief. You can't cut that out of scripture no matter what your theology is.
So to your original question which was this:
"Can a human choose not to believe and thus thwart the will of God in all other aspects of salvation?"
The nuanced answer, taking into account my theology and other verses in scripture has already been given. For you my answer is of course "Yes", or else Jesus has to be wrong in the verses quoted above. The biggest problem with Calvinistic theology is that it seems to me that is unsuited to many folks mind set. That's why I say if you are one of those folks then just reject it and go on. For all I know, you may be right and I'm wrong. But I have also discovered that this holds true for some who identify as Calvinists also. So you end up overstating certain aspects of Calvinism and could actually do great damage in theological discussion.