We have the MX-5 on an intelligent Oxford charger seems to work fine without disconnecting the battery. Only caution is routing the cable so you can't forget about it before backing out of the garage.
I don't think a dumb trickle charger would do any damage at all either, as most components are isolated by ignition and relays when parked up, plus the alternator is effectively a charger and that does no harm to components while driving. A full battery would not take any charge from a basic trickle charger, although a faulty battery might draw currents higher than desired.
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TG