Should captured pieces remain visible? I don't think there's a rule about this, but maybe it's a matter of etiquette. Nearly every player I've encountered puts the pieces they capture next to the board, but I've met some who like to store the pieces as soon as they capture them (maybe they are "neat freaks"? :-).

I found this a bit unsettling, but maybe it's just me? I must admit that I semi-consciously use the captured pieces for counting in the early parts of the game, when most of the pieces are still on the board. I also suppose that it could be inconvenient to have to ask the other player to dig out your dead queen in case of a promotion (that situation didn't arise in my experience, however).
There is certainly no explicit rule about this, and players often fiddle with captured pieces (e.g. Boris Gelfand can often be seen twirling a pawn by its head).

However, pieces should remain accessible to your opponent in case of a promotion, particularly in blitz; at some events (usually the higher level), players are given an extra queen, but not all tournament organizers have that many extra queens!

Having said so, it looks like your question is in the context of a friendly game, presumably where the box/pouch is just next to the board. In that case, if you need to see the captured pieces as a counting aid, just ask!