Well, if the rebellion succeeded, and that's a big if, Thomas had already adopted a co-emperor, and then another, after the first was killed IIRC, so the succession was there. How capable this successor was is another issue, almost nothing is known about him. Much would depend on how long Thomas himself would live after his victory. BTW, one version of the story has Thomas claiming to be the deposed Constantine VI, so if this is actually true he might claim that he is the continuation of the Amorian dynasty, which would certainly come in handy regarding his legitimacy.
As for iconoclasm, Thomas' anti-iconoclast credentials are probably more the result of later pro-iconophile propaganda rather than an actual policy of his. As a close friend of Leo V he may have been pro-iconoclast himself, but with his hold on power shaky I'd think he'd adopt a more non-confrontational stance. I certainly don't think we would see the active promotion of iconoclasm as under Theophilus.
Then there is the issue of his promises to the Caliphate in exchange for Arab support. No-one knows what they were, and if he is feeling lucky he might try to pull off a Leo III, especially with the Caliphate being in turmoil at the time, but then again he might not. I think the most realistic outcome would be the payment of some form of tribute, that al-Mamun could use in his propaganda. Perhaps also some border fortresses in Armenia might change hands. If Thomas' victory were quick enough, it might be even sufficient to butterfly away the Muslim conquest of Crete, and sparing the imperial military from the losses suffered would doubtless also help in preventing the beginning of the conquest of Sicily as well.