In all the interviews I've seen with UCONN players, it's clear that they ARE aware of records, awards, etc. In general they don't publicly chase season ending individual awards, but when I see quotes from KML talking about how "breaking Dee's 3-point record means so much" to her and Kiah talk about being mentioned in the same sentence as Rebecca Lobo, it's clear the players have a sense of history and individual accomplishments, even if they don't publicly chase those as "stated goals".
And maybe we as fans are much more excited about the individual awards than the players are. BUT I do think the players know exactly who wins what awards.....