Site-built deck drainage
Here is an article in Fine-homebuilding on site-built deck drainage.
![Rubber roofing drainage](https://i.stack.imgur.com/gFbMF.jpg)
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.
![Timbertech Dryspace](https://i.stack.imgur.com/sczPG.jpg)
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.
![enter image description here](https://i.stack.imgur.com/39rdx.jpg)
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
![Torch-down sleeper deck](https://i.stack.imgur.com/pXTje.jpg)
Pressure treated lumber can get warped if left out in the sun. But my experience is that if the lumber is used in an application where it is bolted onto place and secured with proper fasteners that it will work just fine. There is no doubt that certain suppliers of PT lumber are applying the treatment to the lesser grades of the wood.
Best Answer
I would say crown side up and shed water. The deck that was on my house when I bought it was cup side up and is in horrible shape. That could be from the fact that the people never took care of it but being in a rather wet/snowy climate didn't help. I'm sure pooled water of any kind can't be good, even on treated wood.