Well, it certainly can and it does, for us. All depends on your usage patterns and having enough PV and battery.
I'll assume you mean kWh, not kW. If so, then yes, I agree that is looks do-able. I must say 6kWh is a very atypical low consumption and I wasn't factoring that in with earlier comment. You're using an average of only 250W, including water heating!
Obviously you've done your calculations on usage and your figure of 16kWh concurs with the PVGIS figures for your location (
JRC Photovoltaic Geographical Information System (PVGIS) - European Commission)
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My 2p worth would be that having such a low household usage it will be most efficient to max out what power your inverter can deliver from solar + battery on the sunny days - i.e. being able to charge at the greatest possible rate will minimises losses within the EV due to its fixed quiescent draw when charging. So, if for example, your inverter can deliver 6.2kW and household usage is normally around 250W, then you should be able to dump up to 24A (around 5.7kW) into the EV once your batteries are getting full and your water heated up - even if that is only for 2 to 3 hours each early afternoon