I think we know more accurately than a few million years. Betelgeuse has already expanded into a red supergiant, which means it has exhausted the hydrogen in its core and moved on to the helium burning phase and possibly beyond. In a star the mass of Betelgeuse (about 20 times the mass of the sun), this phase only lasts on the order of a hundred thousand years. So it should blow within the next few hundred thousand years, possibly tomorrow.
Yes, it's true it will take the light 600 years to reach us after it blows, but it might have blown 599 years, 364 days ago, so we could see it go off tomorrow.
In terms of how it would increase our knowledge of supernovae, it would have a huge impact. Here are two ways. First, since we have studied Betelgeuse extensively, we know a lot about it before it goes off. There are only a few supernovae where we have information on the star before it blew - usually we only find them when they explode. So this would help a lot to refine the models of which types of stars give rise to which types of supernovae. Second, we would learn a lot about the core collapse from the neutrino emissions, which come directly from the core. For SN1987A, we measured ~25 neutrinos here on Earth when it went off. But because Betelgeuse is so much closer, and because the neutrino detectors are so much better than they were in 1987, we would measure many thousands of neutrinos. This would give us neutrino energy spectra and neutrino light curves, which would tell us a lot about the details of the explosion as the core collapses. The light we see comes from the cloud of expanding gas far outside the actual explosion, but the neutrinos 'free stream' directly out from the core collapse itself.
I hope it (or another star in our galaxy) goes off in my lifetime. As has been said, the last one in our galaxy was in 1604, so we are 'due'.
BTW, I have an astronomer friend who has nightmares that Betelgeuse will go off while his telescope is down for maintenance!
