I read very conflicting accounts regarding this. I have an iphone 4 and updated to iOS6 yesterday.
I've updated apps, gotten free apps that weren't on my phone before and never did I have to type in my password. The only time I remember typing my password was to verify my id right after the update.
EDIT: I think it did get changed. Thats funny as I downloaded some free apps in the morning that I never had and it didn't ask for any password. I just checked again right now and it prompted me for the password. First time after verification it asked me.