No,
not yet at least.
1. Hes not dead.
2. hes not part of a squad
3. And three if he were to die, go to shinigami school, actually learn to control his reiatsu, And learn to use Kido he would be much stronger than any captain.
Well he can if he wanted to
1. he could take the captians test meaning you must demnostrate mastery over a bonkai and fight a captian while 3 or more caotians watch 1 of them must be the head captian
2. he could got to the squad he wants to be captian of and fight the captian 1 on 1 with 200 or more squad members watching and if he kills the captian he will become captian of that squad
3. personal recamdenation he has to be recanized by 6 captians and get aproval from 4 of the remaining 7
so yes he could be a captian because of any of these methods
well he could but the only way he could do it is to challenge and kill a capitan in front of at leats two other people which he could absolutly do if he wanted but he dosen't and otherwise he doesn't meat the qulifications seeing as he's not dead but someone stated earlier the he's not in a squad and that is incorrect technicly he is in squad 13 but he's not seated or anything