You get sulphation when you run a battery low and leave it there. Crystals form which short the lead plates, which reduces the battery capacity.
Alternator (driving) charging is fast but a little crude. After a while you end up with small imbalances in each individial cell inside the battery. No problem with sulphation here, just you lose a little capacity.
When you plug a battery into a mains charger with a trickle charge (float charge) facility (they pretty much all do) it charges the battery at max power, then as it nears full it tops up with a lower current charge which allows the cells to all become totally full, then it switches to a float charge - this is a very low current charge to allow for the fact batteries self discharge over time. Some people call this a maintenance charge.
Going back to sulphation. Over the years of being used, and occasionally drained too low, your battery might accumulate sulphation, decreasing its capacity/performance. Another form of maintenance charge called "desulphation" (unsurprisingly) can be run to try to fix this problem. The charger does this by charging the battery at a much higher voltage (not current) than normal - perhaps up to 20v, for a reasonable short period of time. The idea is this high voltage charge disturbs, and breaks down the lead sulphate crystals.
This option is disabled by default in most solar regulators as it is nor intended nor good for AGM batteries. It can also produce a fair amount of flamable gas when being performed on regaular batteries if they start venting at 20volts or so.
I have always left lead acid batteries on trickle (float) charge for all of the time where possible. It means they will never drop under 10v, which is the real battery killer, and they are always full. Solar regulators all drop to a trickle (float) charge when the battery is full. As should all mains chargers except the old style from yonks back. I can only assume the cali built in one does, otherwise there would be a lot of exploded overcharged batteries
So I'd leave the hookup plugged in as long as it suits. It's no difference from having a solar regulator/charger. As you are plugged in your batteries won't self discharge at all. Just check the VW charger spec to ensure it is a 3 stage charger (bulk, top-up, float)