Should I fill my crawlspace drainage trenches before putting down a moisture barrier?
I think you want to insure good drainage under the plastic sheeting. I don't think it's a good idea to leave the channels to fill or to collapse. 

At some point work in the crawl space might be required to repair plumbing and hidden channels under plastic sheeting might cause problems. 

Flexible porous plastic drainage pipe in the existing channels might be a better solution than crushed rock. It would be very lightweight and easier to install.

I have seen advertisement for porous rubber block system that claims this system to be superior to "French drains". These blocks would presumably not need filling on top, but might be stiff and hard to get into the crawl space.

Both of the above would probably require the channels to be cleaned out and maybe deepened a little.