Does anything specific happen when you build all the imperial levels?

Tiny Death Star is still receiving updates occasionally, which add more levels - including Imperial levels. It's certainly possible that such a new Imperial level might enable you to complete this mission in the future.

It is also very much possible for the emperor to ask for a currently impossible level to be built. This could be considered an oversight or a bug - neither of these is confirmed and we can't really look into the developers' minds on this. Support for Tiny Death Star is also abysmal.

If you wish to proceed with the missions, you will either have to wait for an update that adds Imperial levels, or skip the (costly) mission.