No, the position in the sentence does not change the meaning. ‘While’ has both meanings (indicating either contrast or co-occurrence) in both positions in the sentence.
Or rather, to be more exact, ‘while’ only has one position in the sentence: at the very head (start) of the clause. The difference in your two examples is the order of the main clause and the subordinate clause—and this order makes no difference for ‘while’. The only thing that determines what ‘while’ has is context, as with so many other things:
1a: I hate to watch TV, while my wife loves it.
1a: While my wife loves to watch TV, I hate it.
2a: My wife talked about her day while I had lunch.
2b: While I had lunch, my wife talked about her day.
Sentences A and B in both these pairs mean the exact same thing, regardless of the order of the clauses.
In A, where the subordinate clause follows the main clause, there is a natural pause in speech separating the clauses when the meaning is one of contrast, but (usually) not when it is one of co-occurrence. As such, you can distinguish the two meanings fairly clearly by adding a comma in the contrastive case.
In B, where the subordinate clause precedes the main clause, there is always a natural pause in speech between the clauses, and a comma nearly always sets the two apart, so the ambiguity remains.
There is one way you can often force the co-occurrent sense to prevail: by using a progressive verb form in the subordinate clause and a non-progressive one in the main clause. In cases where the meaning is contrastive, this can sometimes be quite impossible, but it is always possible where the sense is one of co-occurrence:
1: I hate to watch TV while my wife is loving it. ✘
2: My wife talked about her day while I was having lunch. ✔
This does not always work, though (especially when the subordinate clause heads the sentence—one instance where it appears the order of the clauses does make a difference):
3: While I was living in squalor, my brother mingled with celebs and the nouveau riche.
This example could show either co-occurrence or contrast, but will most likely be understood contrastively.