If you choose to keep riding this bike (not generally recommended), know this:
By imposing a permanent deformation on the aluminum, you've over stressed it.
From a fatigue damage perspective, this is one of the most damaging things you can do (think bending a paper clip back and forth - it doesn't take too many times to cause it to break, compared to just gently flexing it without permanently bending, it takes thousands and thousands of cycles to cause it to crack and break). And recall, aluminum isn't as good as steel in fatigue (in the general sense - no nitpicking from other engineers, this is for a lay audience).
If you are going to ride this bike, consider, as suggested, having a post long enough to go below the damage. That way, if it breaks, the worst likely outcome is the seat drops instead of totally falling off.
Do a close visual inspection of the damaged area frequently - probably before and after each ride, to see if you can see any cracks in the area. Run a finger nail over the area feeling for a crack. If you detect a crack, scrap it if a competent welder can't repair the area.
Or just look at this as an opportunity to upgrade.......