FrogReaver
The most respectful and polite poster ever
I think 2 things.If the GM tells the players that their PCs are at a dead end, that will affect roleplay: as per @FrogReaver's post upthread.
In general, the state of the fiction - both internal and external elements of it - will affect roleplay.
1. there's still a scope issue. Being at a dead end is going to affect my roleplay in one moment or one scene at most. Your character's beliefs are going to shape your roleplay over the whole campaign.
2. Whether or not you wish to acknowledge it, there's a difference between the physical and mental that gets brushed aside by you as if there is no difference at all.