The TEC AI has a chance with Ogrov spam, but usually it will have long-since gimped itself via continual suicide charges by the time it actually cracks that starbase.  Advent and Vasari... forget about it on hard difficulty.  Maybe they'll stand a chance if you don't have repair platforms nearby, but that will probably require a few failed attempts to wear it down first before they finally crack it.  So yeah, In general these starbases are virtually impregnable.  There is a slim chance one might go down, but it's going to take some ridiculous number of units to do so.

If we're talking about an Advent starbase with the meteor control ability or a Vasari starbase with deflectors or debris vortex then I sincerely doubt the AI will ever beat that monster, and if you leave a few support units to back up that starbase then it's virtually impregnable.  Most human players wouldn't even attempt to take on these monsters without around 100 squads of bombers, an amount the AI will never accumulate, much less use effectively.

Generally yes, if you manage to starbase a good choke point world, the game is over unless you're up against something like a vicious or cruel AI. 

I've been asking for an AI improvement to better challenge players once these kinds of starbases are operational, but I just don't think it's in the budget sadly.

If you don't leave defenders, then yes a max level pirate attack would be trouble.  Of course, unless the world is literally right next to the pirate base, you have time to get support in there.

The biggest problem with the "max level pirates" argument is that however much they may inconvenience a human player, they completely annihilate an AI.

I made a mod for myself where I just changed the cooldown for a Solanus down to one, as an experiment. Ten Solanus killed a fully upgraded Argonev. It was funny.