Trex decking is put down with a space, usually 1/4", between the boards. This is because the decking has a much higher expansion rate then the deck structure. The spaces allow the deck boards to expand and contract. If you fill the spaces with something soft and flexible it may deteriorate after a bunch of expansion and contraction cycles, that would be a mess and very difficult to clean up.
If you have enough height I would recommend a sub roof under the deck that would channel any water away. Use sheets of corrugated fiberglass panels.