It has a pretty obvious mark under the name if they are verified.
That said, I did ask the few people I know that have been using BAT. All three of them knew that there was a chance their tip wouldn't be received if it wasn't a verified user. So, from actual users, putting actual money into it, they understood how it worked.
Two of them specifically would only tip to verified accounts. The third said he saw it as an incentive to get the creators to join the platform, though he's also the most vocal and evangelistic about BAT.
It has a grayed out message and a link to learn more about what happens to unclaimed funds: http://se.ri0.us/2018-12-23-170628027-eb454.png
"Not yet verified" would, I think, imply to many people that they will in the natural course of things be verified, and perhaps even that they've asked to be verified.
It would be better to say "Bla is not a user and will not get the money you donate now, and quite possibly not ever", or similar wording. Or just (and this is, er, the obvious approach) not allow this at all for people who haven't asked for it.