Yes, not only can you do it, that's how it's actually done. The space probes which have used ion engines (Deep Space 1, SMART-1, MUSES-C) were all launched by rockets using conventional propellent. The second or third stage motors put the probes into a parking orbit or sent them on their merry way and then dropped off. The propellent burns were on the order of minutes, the ion engines then "burned" for weeks, or months or years!!
If you were designing a probe to go to Pluto or Alpha Centauri, you would want the biggest, most powerful conventional rocket motor you could afford to give yourself a kickstart. Once the fuel is exhausted you'd want to dump the motor and the fuel tanks and allow the ion engine to kick in. As mezerashi pointed out, the actual thrust of the ion engine is rather feeble. There's no point in carrying the excess mass of the conventional motor and depleted tanks with you. I'll leave out the 432 potential problems in mounting such a mission, but you probably get the drift.
If you're so inclined, look up MUSES-C (aka Hayabusa). It's an ambitious JAXA project which uses an advanced ion engine to send a probe to an asteroid, deploy a hopper, collect a sample, and then return it to earth. It has been slowly sneaking up on the asteroid with it's ion engine for several months now. It actually uses small conventional motors on its final approach, but will revert back to ion power to send itself back to earth with the sample cannister. Neat stuff!!
http://www.isas.ac.jp/e/enterp/missions/hayabusa/index.shtml