It should be ok, but it will really depend on the bumper itself. Your new bumper will need to have the same clearance zones (up/down) and side to side and the bumper will need to not be to much taller that it would interfere with the base plate connection points. I've talked with easily a dozen owners with such setups and all worked fine they said. If you are order one of the more name brand bumpers you can probably find somebody with one that can vouch for the setup on many Jeep groups. In some cases you can probably get that question answered by the base plate manufacturer itself.
If you have a specific bumper in mind post it up here might find somebody with that setup already that can help you out.
Two Wire Fox Terriers; Sarge & Sully
2007 Winnebago Sightseer 35J
2020 Jeep Gladiator Rubicon