There are several problems with this that I can see.
First Snorlax's sub needs to be able to survive one hit. Yes, Snorlax is bulky, but still a hit from any reasonably powerful Pokemon should still take out the sub.
Second Trick Room only lasts 5 turns, and as Snorlax can't use it itself it would need to switch out to the Trick Room user every time it runs out, which negates the Belly Drum, and means you have to do the whole sub + Belly Drum again.
Third, sub takes off 1/4 of your HP, and Belly Drum takes off 1/2 your HP. 1/4 + 1/2 = 3/4 of your max HP gone, so Snorlax will have only 1/4 of its health remaining, or slightly more factoring in leftovers recovery. And that is assuming it took no damage switching in. So by this stage any hit will probably take out Snorlax, or two at the most. And before you say "but Trick Room is up, so Snorlax will go first," then you are forgetting about priority moves. Mach Punch, Sucker Punch, and Extreme Speed are particularly dangerous, although the other priority moves could get the job done. Also while Snorlax is slow, there are other Pokemon just as slow, if not slower, so they might be able to go first without priority. This includes Pokemon like Ferrothorn, Steelix, and Shuckle.
So there is just three reasons why this is not a good idea in practise.