Ouch! i would hate to think how much income your going to be forced to loose when you have to turn down taxation once you start taking AI worlds!
Depends how you treat those worlds (amongst many other factors, I'm sure).
AI worlds usually have a starport - if you use up the production already tied up in it then remove it, that saves some bc.
If you remove all unnecessary structures (usually any +moreale, +influence, OFM, defense) that saves some bc.
If you halt upgrading of structures, that saves bc (often you already have all the research and production you need, so upgrading those types of structures is pointless). You might let factory type buildings upgrade if there's a lot of building or refitting to be done. But you might also move those down the queue and build some stock markets ahead of them so the world can pay for itself quickly.
It also helps if you put some people on a newly conquered world so it has some taxpayers and repopulates faster. The biggest reason conquested planets generate no money and crush your econ is lack of people to pay taxes. I'll usually dump and extra 1b on after an invasion.
Then you start adding stock markets or replacing other structures with stock markets.
And you have a new money world to pay for your core and warships that doesn't ever really cost you much or costs nothing.
You probably won't always convert a newly acquired world to a money world but unless you have a definite plan for it as a research or production world, then it's probably a good idea and it'll help keep your "expansion costs" under control.
I haven't played on anything bigger than large maps so far though (PC could handle it, but dunno if I could!). I'm not sure I'd enjoy the micromanagement involved with a 300-500 planet empire.