In my experience, yes. It will stay as blocked. That's why most of the non-wool yarn instructions say to machine wash AND machine dry on low.
PS - Whoops! I just saw your word, Cotton. That changes things dramatically - my experience is almost entirely with acrylic fiber yarns. Wool, not familiar. The only cotton I've knitted with is either for dishcloths or for socks; and cotton yarn for socks is entirely too un-stretchy for me to recommend it to anyone else for this use.
But as a sweater? I'd think that un-stretchiness would make stretching and blocking not real successful from the get-go. Again, I've not really done that, so maybe someone more cotton-yarn-experienced would be better able to answer.