I think stars will continue to orbit. The check options for body orbits are really intended to be used for reducing computational load of calculating all those orbits (so performance should actually improve, at least in that way). Stellar orbits are so few that they have a minimal effect anyways, which is why they aren't given as an option - I don't think Steve anticipated such an "insane idea"!
I would say to have most of the setup be based on planets orbiting a single star - three planets at the same radius with 120-degree offset is probably unrealistic but would be Fair and Balanced™. However a far-out orbiting star could be interesting as the home of a human-controlled "spoiler" race that periodically raids or attacks in-system, adding some temporal element to the proceedings although maybe it is too far away and the orbit would be too slow, so one race would suffer disproportionately.
In terms of performance the only concern I can think of would be sensors and detection, since everyone is in the same system detection would always be checked and this can be quite expensive especially with a lot of fleets...I think disabling civilian fleets is a must here.
I would also suggest to be aware of how small ranges can actually be... typical ships that players build have only 20-30b km ranges but also only 1:10 or 1:12 fuel-to-engine size ratios when using 1.0x EP modifiers, where 1:3 is optimal so ranges can easily be 3-4x this even with military engines. There are some interesting options in the DB modding direction you can try (or even combine) to make space truly feel smaller: cutting fuel efficiency (I have tried as much as 1/20 reduction and it certainly shrinks space when you cannot travel so far!) and/or cutting engine power - the latter I have tried at 1/5 vanilla values, and it is interesting but changes a lot of other balance aspects, notably beam weapon ranges become far more significant giving lasers and particle beams a much larger advantage over railguns for example, not to mention missiles being extremely vulnerable to area defensive fire. You can quickly get stuck down the rabbit hole of further balance changes, but it can also be quite interesting what kind of game results and the ship designs you develop.
