A 3000 frigories A/C takes around 1.2KW, more than enough for a living room. That is 4 panels with 450w each with some headroom.I've thought about it. Supposing a small 2.5kW unit, you need about 16 sq meters of panels (about 5kWc). Without a battery, I'm not sure the compressor would even start.
For the “in rush” moment there is a device called “soft starter” wich is used in well pumps. It delivers current slowly, the pump starts spining also slowly and it doesn’t have the peak current.