There's a balance between quality and quantity required, of course. In the UK, the OBS>S1 training takes people less than 6 weeks in most cases, dependent on their availablilty, and as a result we see that pretty much every airport that gets any planes is staffed with at least GND during the majority of the local "peak times"; I don't necessarily think it's possible to beat that.
However, from APP up the story is slightly different; due in part to a lack of mentors, but also a whole set of other factors, the time taken for S2>S3 and S3>C1 is exponentially longer than lower ratings. It's not helped by the lack of mentors to run it, but it is ultimately as a result of the skills being required of these people being much more difficult to learn quickly.
The UK, and other european FIRs are an exception in their high traffic levels and ATC staffing (the same isn't seen on IVAO, at least not in the same locations). VATSIM has a shortage of ATCOs in many areas of the globe, and at many times of day, but I think that's as a result of people who fly in different countries choosing IVAO over VATSIM. If you merge the ATCS coverage of both networks, you get a pretty good spread both spatially and temporally ; I don't think that's related to training though.