I had a concrete driveway poured and gas line run to pool heater with no permit. I'm sure I got lucky though as the village had dickweeds always driving around looking for that shit.
It's possible. The last robotic one I bought was only $300 and that was probably 10 years ago. I returned 2 and sold the last one after trying them several times. I'm sure the ones now are pretty good.
It would take me 30-40 minutes to vacuum the pool (28' round). I was OCD and wore a mask and snorkel and got every last bit of everything. I'd have the tunes jamming on the outdoor deck speakers so it wasnt bad.