My schematic is a theoretical concept, rather than being complete and ready-to-build. It lacks many details. It may even be totally unrealistic.
Example, can your mains AC provide pulses of 23A? Would a circuit breaker trip?
This amount of Amperes should not be applied to a single capacitor, but should be shared by a bank of capacitors. Can you obtain sufficient capacitors which are rated for 400VDC? (Because voltage will rise to 330V when there is a light load.)
High voltage is an obvious risk. As well as the risk of ruining a big expensive air conditioner.
A motorized appliance can generate spikes, back-EMF, etc., which could ruin the H-bridge mosfets.
If a short-circuit were to happen for any reason, it would expose the air conditioner to high voltage DC. I have not heard of this being tried, but I believe it would destroy the appliance.
Also consider what others have replied above. They are more expert than me.