A plugged drain line may indeed be the cause...
You can probably remove the AC units cover on the roof to get to the 'inlet' of the drain - it could be the connection between the line and the AC's drain is detached, rotted, etc...
If you can get to the drain on the roof, you may then be able to purge the line with low pressure water from the garden hose...or try purging from the 'outlet' end of the drain line in the same manner while someone checks up at the AC unit on the roof to see if there's a clear flow....
If the drain line is detached or damaged INSIDE the roof panels, some other method than the garden hose should be used - maybe low pressure air from a compressor, for example...
As I recall when I replaced our AC unit, the drain line was accessible from inside the trailer with the AC panel removed...
Luckily, the Carrier AC unit we used as a replacement doesn't require a drain line - there's a collection pan built into the unit that has airflow directed to it to evaporate the moisture...It's worked fine so far, but we've not had to run it 24/7 as is required in the hot & humid South...