I'm sure a tech-savvy enough person can extract the lengths of all operating coasters from rcdb and total it up. That would give a minimum value (since not all coasters have that data, and it would miss out travelling coasters). From there you could probably estimate the lengths of coasters not included from that extraction.
For a rougher, back of an envelope type calculation...Of the 244 coasters I've ridden, the average length of those coasters with a known length listed on rcdb is about 1754ft. Whether that's an accurate reflection of the average length of a coaster is hard to say: I haven't done many long coasters (when one considers what's out there), but equally there's a lot more Wacky Worms out there than long long coasters, which skews things.
But let's say for argument sake, on average, the average coaster length is 1750ft.
Now rcdb states there's 5543 operating coasters, but that includes shuttle and semi-shuttle coasters (it's unclear if you want to include rides like Star Trek Operation Enterprise and Pantheon). Let's say there's roughly 750 travelling coasters around the world (a loose number gauged between a 30 second look on rcdb and Coaster Count), meaning there's about 6250 operating coasters in the world.
So the total length of all full circuit coasters in the world is around 10,937,500ft.
I'm not clear why shuttle coasters are excluded? Is it because the train would travel the same piece of track multiple times, if so then why not just count it once (which would be the nominal "track length" anyway as per rcdb). And what about full-circuit coasters that you do multiple laps on, you would only count one lap's length for them so why not the length of a shuttle.
There are just too many questions here, this does not sound a very scientifically sound study to me.