It would not be efficient if you are talking about leaving a plastic tarp covering the air conditioner and bathroom fan. The air conditioner works through heat exchange which requires that outside air move over the coils inside of it. If that air cannot escape (it just re-circulates under the tarp), it will build up heat (and moisture) under the tarp and not function well.
Same for the bathroom fan. The air needs to escape into the atmosphere, and to function well there should be an inlet source (say a partly opened window) in the RV where air can come in to be exhausted to the outside. Some air may escape around the sides under the tarp but it really would be best if you remove the tarp before running either the AC or the bathroom fan…
If the roof damage is not too extensive, perhaps you can just cover the damaged part and leave the AC and fan open to the air until you can cover it entirely again. Another alternative might be to put some kind of spacer such as buckets or tires between the tarp and the trailer to provide a clear channel for air to escape.