What inverter are you looking at?
SMA with secure power supply is quite possibly what you're looking at - and there's no benefit to using that outlet to charge your car as opposed to any other outlet in your house.
(With the exception of if there's an actual outage it could maybe charge the car)
If you have (or will have) net metering (most people in US do.)
then you are probably better off doing a 220V charger because it'll likely more efficient.
(At worst it's same efficiency - in which case you're just as well off using 220V as a 110V outlet.)
If you do a time-of-use rate charging at night (off-peak) could be significantly better than charging while the sun is shining.