Sorry to be the bearer of bad news, but there is no magic solution you can spray on and restore the original beauty. As an owner or an older Carver with lots of teak, the only solution is to sand it down. We solved the every year restoral ritual by using Seatrol medium sealer by Sikens. (found in marine stores) Couple of coats of this stuff and your teak will look good for years.
Site-built deck drainage
Here is an article in Fine-homebuilding on site-built deck drainage.
In this article they use EPDM rubber roofing material.
I wouldn't hesitate to use this or creative alternatives, but I wouldn't consider this as a "waterproof/roof" system. I would consider it rain-proof where it diverts rain and rain-runoff from underneath the deck.
Retail deck drainage
There are products available that are designed for this as well. Like Timbertech Dryspace for example.
My opinion
Using either a site-built or retail product, I still wouldn't store anything under there that would be ruined from getting a little bit of moisture now and then.
If you want a real waterproof roof, then build it as a code-approved roof with code-approved materials installed how they were intended to be installed.
Issues
One potential issue I can think of right off the bat is that dirt and debris will collect in there, so do you have a plan on cleaning this out? You will need access from time to time to at least stick a hose at the highest part to rinse it out.
Another potential issue is that this would limit the airflow and potentially increase the humidity between the decking and drainage material. This could contribute to things like cupping or premature finish failure on wood decking.
Real Roof (info as requested in comments)
60mil vinyl can be considered an approved roofing surface. You would use something like this if you are not putting another surface over the deck.
Another roofing option (if you wanted to add wood planks) would be to do flat roof (i prefer a torch-down roof): then build panels out of your deck surface, or attach the decking to sleepers (see image below), or use wood tiles
Best Answer
I have installed membranes underneath decks and ran them to gutters to provide an under deck patio space. To answer your question, no you can't do that - for the easiest reason - because it won't work and your guests will get wet. And for a hard reason, it will tear up your deck with wood expanding and warping due to pressure or wood rotting due to standing water.
I would ask a follow up question that asks possible ways to divert water, so that people can answer that.