Aldridge visiting Boston probably means he's going to the cavs. Thats usually what happens when star bigs visit Boston. Plus, the Cavs will be in need of a big man after Kevin love signs with the lakers.
It would be very very difficult even then.
Picture this, with only Lebron and Kyrie under contract, they would be able to do it. Otherwise, they won't be able to afford him, unless Aldridge takes a pay cut. Hard to see.
That means before going into free-agency, the Cavs would need to be 100% sure Aldridge was coming over because they need to trade away guaranteed contracts (most are one years so it shouldn't be too difficult, though I don't know if they have future draft picks to offer).
There are a lot of X factors to clean up the whole roster, and even then I haven't calculated the cap hold for empty roster spots, so that's something to keep in mind.
Here are some difficult problems:
Mozgov's team option needs to be exercised by June 30 last I checked, not sure what rules follow up that decision in order to be able to trade him, if any.
Smith has a player option, I don't know on what date he can exercise that option.
Thompson would need to be offered a qualifying offer at some point, or forgo it. That should complicate matters.
Any of these issues, to say nothing about salary dumping everyone else, will make it impossible for the Cavs to offer Aldrige a Max contract.
So in all, Love leaving Cleveland would not open up the opportunity for another Max player to enter the equation, maybe next year when the cap goes up, but not now.