Yes - I think you're right, though the Renault Master which the campervan is based on does have a 150 amp alternator. Again my carefullness suggests one battery at a time! I will probably get the 600w inverter and see what power it pulls when charging one battery (via the van's NASA BM1 battery monitor), then maybe consider charging 2 at a time.
Kendalian
My camper van is also a Renault Master, and has the 150amp alternator, the problem with them is, when the alternator sees the engine battery reach 12.8 to13v, the regulator drops the charge back to a trickle 5 to 10 amps, and takes forever to charge them, the setup is designed to power everthing on a journey between campsites where you can hookup to mains, I seldom use campsites, so I have fitted a Sterling 120amp Batter to Battery charger, it draws power from the alternator and boosts it to 120amps, which charges my 550Amh batteries very quickly and the batteries run my 2KW pure sine wave inverter, the inverter also runs tv, sky box, toaster, microwave, laptop ect, solar power charging is fine when its sunny, but the Battery to Battery charger is a good backup and reliable, a 45 min drive will re-charge my batteries.