I think they'd be okay. As @QuentinGeorge says, it would be an interesting way to get around needing to be dex based for AC. I mean, I get that a wood elf monk would be mechanically superior in some ways* but if a tortle monk sounds fun I'd say go for it. The minor benefits you get from race don't really matter all that much outside of white room analysis.
I mean, I probably couldn't do it without doing the TMNT thing to the hilt which would probably get dice thrown at me. On the other hand, who doesn't need more dice? 
*I tried one but it died almost immediately because all elves I play are cursed.
