I don't believe I have tested, I know they go to mailbox if you claim and your storage is full.  Everything else from events goes to mailbox so while I agree it would be silly, I don't think I have risked testing it... But I am guessing you want to save for chase points?

Yup.

In any case, claiming champions from your mailbox doesn't count for champion chase purposes - I tried it with a login reward champion once and while he did go to my mailbox, I didn't get any points when claiming him during the champion chase. 

So you might as well just claim them immediately. 

Ah. Alright, good to know. Thanks!

Though it shouldn't go to mailbox until 24 hours after event, so you could wait on that.  Though I guess it is just 10 pts... lol 

It  gets  the  points  when  claimed-  so  when  sent  to  the  inbox  in  the  first  place.

Looks like they changed the number of days to claim rewards from 1 to 3 days, looking at the recently completed Dragon Tourney.  At least I thought it was 24 hrs before, I could be wrong?  So be easier to get the extra 10 pts in champ chase events going forward:)

Well, I ended up claiming them anyway - 'cause like you said, 10 points isn't exactly a huge deal, lol

Fusing them though will get an epic, which should help get the remaining fragments more easily.