Charging?
Honestly, I don't think it would hurt. But in my opinion, due to the expense of the electronics, I'd disconnect the ground side of your battery before charging, just to be on the safe side. What's the old saying, "better safe than sorry".
Oh, and because charging a battery can emit explosive vapors, I'd leave the engine compartment open. The trickle charge is just a battery maintainer, so there isn't many charging amps going to the battery, but better to overdo than underdo and regret it later.
I've been doing research on your other post, so I'm heading over there now.