Short answer: Probably not in this situation - you may just end up increasing the relative humidity inside the tent.
AC units provide some dehumidification to air as the air flows over their cooling coils, but cooler air also holds less water. For example, if you cool 30°C (86°F) / 80% RH air down to 27°C (81°F) without removing any water, the RH would increase to 100%. I'm not sure the dehumidification provided by a small AC unit inside the tent would offset that....I'd have to re-learn my HVAC
psychrometric charts.
Theoretically, if you have the exhaust of that AC unit venting inside the tent, then technically it should have no net cooling effect (and perhaps, even a net heating effect due to inefficiencies) while providing some dehumidification. I.e., it should act just like a regular dehumidifier (but perhaps less efficient). However, some / most portable AC units are designed to mix in the condensed water with the exhaust instead of collecting it in a tank, which would defeat the purpose here.
You may be better off running your home AC full blast and/or opening windows (if outside RH is lower than inside) to lower your house RH. Otherwise, a medium / large dehumidifier in the lung room would be your preferred solution. Realize that all the water you're adding to your plants is being released into the air and has to be removed somehow. You could try defoliating somewhat to reduce water usage, but that could be playing with fire.
If you already have dehumidifiers running and they're just not keeping up, you could try desiccants as a last-ditch effort...but I can't guarantee it'd work, it's only a short term solution, and it's not cost-effective long-term vs. getting an extra dehumidifier. Desiccants are what are used for rapid-dehumidification in the more expensive commercial dehumidifiers (e.g., for quickly drying out a flooded home). Calcium chloride can absorb up to 3x its weight in water and is sold as rock salt / road & sidewalk de-icer at home improvement stores for ~$20 / 50lbs. You could DIY something on your intake to have the incoming air pass through the rock salt (e.g., in a 5-gal bucket), but that would reduce your overall air flow, could end up blocking the air flow, etc. I'd put that in the "science experiment" category for now.