Do items "found" through Dice Rooms rerolls show as unlocked in the items sheet?

I've asked the same question on the SteamCommunity Forum, and this is the outcome:

Nope, they don't sadly.
I know because I've tried it, was getting nothing but Breakfast which meant I had exhausted the entire pool. But none of the items that I needed to find were in the collection page.

EDIT:

There are different opinions, so it's a bit confusing, another guy posted this answer:

I haven't unlocked these yet and somehow they're there.

Meaning that he hasn't unlocked The Lost items (The Soul, The Body and The Mind) but they are shown in his collection page. So it appears to be true.