In the next movie, Kirk can turn into a tiger. Perfectly reasonable considring all the psuedo-science in Trek. Also, Khan's blood saving some girl has perfectly set up that ability.
Yes. After all, we saw the crew of Enterprise-D devolve into animals ("Genesis"), including Barclay becoming a spider. Data came up with a retro-virus that cured them all.
So, there have been far sillier things in Trek than blood that can restore health and life to someone.
It's just a matter of where one draws the line of "silly." Sobeit.