If the Belmont were to end in a dead heat (and Justify were one of the horses), would that still be considered a Triple Crown for Justify?
As a rule, I think that both horses who finish first in a dead heat are considered to be the (co-)winner. Given that, I would suspect that Justify would be considered to be a Triple Crown winner, though probably with an asterisk.
I’d say it would qualify. If two horses tie for first, they both get first place, and the third horse gets third place. I suspect the high-def photos would be looked at very closely to try and break the tie.
So accordingly that horse would be both a triple crown winner and not at the same time, it would be Schrodinger’s horse 
Let’s not beat a dead horse
Which is exactly what happened when a Breeders Cup Turf Classic race ended in a dead heat - they had multiple copies of a hi-def digital photo printed and reviewed before making the decision.
In the pari-mutuel system, Win bets in a dead head are treated as if they were Place bets; each winning horse’s payout pool would consist of the money bet on the horse plus half of the money bet on the losing horses (after the “take,” of course).
In countries that use bookies, payouts are cut in half - e.g. a 4-1 horse in a dead heat is paid off at 2-1.
Total side note question: do they cut the bouquet of carnations in half as well?