Yes, you can do it. The keg is like a big bottle. I agree about adding some CO2 to make a tight seal, but also to displace whatever oxygen is in there. The yeast should take care of that anyway, but why risk it?
I'd be concerned about having the beer be cloudy after transporting. Depends on the flocculation charcteristics of your yeast. If you want to be safest, go with something like WY1968/WLP002 (probably too late for your question since it sounds like the beer is already made). Get that cold and it drops out quickly and completely.
But if you have the CO2, I don't know why you wouldn't just force carb it. It's easy and you have more control.
Maybe if you do it the way you want, you can fine it and transfer it to another keg before moving it to address the potential clarity problem. Or crash cool the yeast after it's carbonated and then transfer it. To transfer, just use a beer-to-beer jumper between kegs and push it into a sanitized, pressurized keg. Make sure it's pouring bright before transferring. Watch the jumper tube to see if it's bright during transfer (a flashlight helps). Then you're removing the beer from all the sediment in the first keg that's likely to get kicked up when you move it. Something to consider if you do it your way. Certainly easier than using plate filters.