Does the collectibles still show up when pausing the game?

What do you mean? Like when you pause the game and go away do they still show up?

Yes, to your question. In both VV1 & 2, I seam to recall them showing up when the game was paused, which I hope doesn't happen in VV3. It sort of defeats pausing the game.

Today I paused the game as I went to lunch. When I came back (the game was still paused) I found a rare collectible (which was missing in my collection). I dropped a child on it and unpaused the game. So I guess the answer is yes.