Sure you could. Each local area (such as a planet) is a single timezone, and everyone there experiences time at the same rate. Someone leaving that timezone would experience time dilation... But in game it would just appear as a communications lag, just as it is for people on different planets. Then, once you've arrived at your destination, there's no longer any lag with your new timezone, and your lag with the original time zone is now fully synched with everyone else on your new planet.

Player A remains on planet A. Player B remains on planet B. Player C commutes between planets A and B, accelerating hard enough for measurable time dilation.