Yes, easily. Solar escape delta-v is about 21 km/s from earth orbit (not including earth's gravity). The Jupiter Icy Moons Orbiter is designed with a delta-v twice that, 40 km/s, using nuclear-powered ion thrusters. To be used to maneuver within Jupiter's gravity well, moving from one moon to another.

http://www.lpi.usra.edu/meetings/jimo2003/hartman.pdf

It's a completely doable project sidelined by budget priorities (NASA thinking space tourism more important than science).