Does the iPhone ask for iCloud password after updating to iOS 8.1?
Yes, you will be required to verify your account when you first log in. 

I would suggest trying to get to the bottom of it BEFORE you upgrade, it will be harder after (since you should still have some access to email accounts etc).

Also, I would research the effects of running iOS8 on an iPhone 4S. Although it may be supported, I would think it would be incredibly slow.

I know you didn't ask for the second part of this answer, but I would strongly recommend you do some more research on this before blindly doing it.