Taking Myr, Tyrosh, Lys, and the Disputed Lands would be a prolonged affair – in addition to the naval campaign necessary to knock out their fleets, and the land campaign against the free companies they’re going to hire, the cities themselves will involve three major sieges, all of which are going to require siege works on land and a naval blockade to cut off the cities from resupply and reinforcement. And that’s assuming that everyone else – Braavos, Pentos, Volantis, etc. – stays out of it. 

I don’t think Daemon himself had the discipline for it – as we saw with the Stepstones, Daemon doesn’t have the patience for sticking it out for a whole campaign, and other than Corlys, didn’t seem to have anyone around him capable of leading in his absence.

So while he’d definitely enjoy some early successes, I think he’d lose interest a year in, and then the war effort would completely collapse in his absence.