Should work like a champ. But then, so would rigging your tarp with a low side for water to run off of into a container...
I have tried a conventional tarp to collect rainwater and found getting the water off the tarp into a container to be a problem. particularly on long runs of tarp as the rate of flow onto the tarp increases it starts cascading sideways. As long as your around you can move the container to compensate but it can be a full time job. It isn't too much of an issue if the distance between the tarp and the container is very small and the opening into your collection basin wide but the tarp has to be kept low or the container held high if you don't want to have to keep adjusting the placement of the bucket to keep it under the flow.
The drain in the center of the tarp and hose makes the water flow much easier to control and limits splash. It also allows the use of a clamp on the hose to stop the flow temporarily. You wouldn't want to stop it for long because it would drag down or damage the tarp. Also if pieces of the ceiling or other debris come down it would be possible for the drain unit to clog and the tarp to become a suspended pool that could let go with spectacular results.