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Possible, yes. But you'd have to talk to Rob if you want something like that to be officially sanctioned (for RNRS purposes).

The best thing to do is to set up an "unofficial T2 online tournament" and run it for 6 months or so.  ROOT was actually started as an official tournament after Soul Seeker had already run the "substitute online tournament" for about 6 months first.  That gave him time to build up a large enough player base to have a consistent tournament, and also allowed him to tweak the format enough to get it into shape as something that was fair, fun, and manageable to maintain.

It was AFTER all this ground work that I was able to approach Rob, and make a solid case for the existence of ROOT based on that model.  So I would encourage you to do the same thing.  Come up with a model, run it for a while to make sure that there are enough players, that your model works, and that you are willing to dedicate the time it takes to keep something like that running.

With the current format their would only be two games a month

I don't know where you get that.  The current format has 1 game a week, which would be 4 a month.

and if two players are paired up in normal root then they could simply choose to play one game of type two and have it count for both.

ROOT has always allowed both players of a ROOT game to choose to play T2 instead of T1 as long as they both agree to it.

I'd say go for it.  Especially if you don't care about RNRS points or being official.  You should just start a thread about it, and see who signs up.  Decide whether you want to donate prize support for a while personally, or whether it'll be just for fun.  If you're looking for someone else to help you run things, Crustpope mentioned a long time ago that he was interested in something like this, and he might be willing to help you out.