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It's possible if the battery is almost full to top it off
However if it needs a good charge the answer would be no. It would take days if not longer and it would be bad for the battery long term if continually charged that way.
Most 12v lines on the trailer connector have an amp limit, but it varies with the vehicle. 10A-20A is typical, but I've seen 30A too. Most trailer side connections connect that +12v direct to the trailer battery (no controller), so you get some charging whenever yu tow.