I think you can do a flat century in three months training, I've done that -- but a hilly one may be a different matter. Sounds like you're in good shape, though, so if you're really motivated, and especially if you're young (or relatively so) and willing to put the training time in, it's certainly not out of the question. But you need to start training outdoors now, I think, if that's at all possible. If you can't get outdoors until April, it's going to be much, much harder, and you risk injury by doing too much, too fast.
Let us know what you decide to do! Is there a shorter option on the same ride, say, a metric century or a half-century, you could do to start with? Most new riders start with a metric, or even a half-metric, before doing their first century. It helps to gain experience with a shorter distance on an organized ride before heading out on a century. You'll be riding with less experienced riders like yourself on the shorter routes, and will probably feel a lot more comfortable during and AFTER the ride!
Good luck,
Emily
Emily
2011 Jamis Dakar XC "Toto" - Selle Italia Ldy Gel Flow
2007 Trek Pilot 5.0 WSD "Gloria" - Selle Italia Diva Gel Flow
2004 Bike Friday Petite Pocket Crusoe - Selle Italia Diva Gel Flow