Sure, you can do that. Of course you won't have the skimmers skimming the surface any more. Typically with a setup like that you would normally leave them all on. That mixes the deep water with the surface water, which can help circulation. There is, however, plenty of flexibility when they are all independent like that. The only things that would cause real problems is turning them all off or turning everything off but one skimmer and having that skimmer get clogged.
The last few days, skimmers have been really filling up with frogs. That got me to thinking...what would happen if we were gone for a few days and skimmers got too clogged for pump to operate. If that happened, would main drain pipes take over?
During normal operation I leave all valves fully opened. This provides a balanced draw of water from the surface and from the bottom.
If you just run bottom only, you probably won't have any issues since you have 2 main drains, but I'd recommend leaving them all on.
As a side note: Try to never run with only skimmers (no main drain(s)). If you do this you will end up with circulation problems and the water on the bottom of the pool not getting circulated. While not terribly likely, it could give algae a better chance of getting started on the bottom and sides.
If for some reason your skimmers do get completely clogged and you have your main drains opened, you will be fine until you get back to clean things out. You would probably be surprised at how hard it is to get your skimmer completely clogged (unless you use socks - much easier for clogs with socks).