Speaking to Eurogamer (via Ars Technica) at the Star Wars: The Old Republic press event, LucasArts executive Tom Nichols said, "We have many other features planned to support Star Wars Galaxies. We see no reason why the two games can't exist together."
Presumably referring to the backlash surrounding Galaxies' "New Game Enhancements" overhaul, Nichols said, "We've learned how important it is to listen to your community and act on that feedback."
Canononically, the two games can simultaneously exist as they take place thousands of years apart, but the real tests will be in the similarities and differences in game mechanics and the continued support of Sony's now three-and-a-half year-old MMO with a tumultuous past. Regardless, I'd personally prefer some kind of shared subsciption fee, but considering that the games are from two different publishers, that seems extremely unlikely.