I can't see how doing both would not mix you up - making your Aikido rigid and sluggish and/or your Karate soft and irresolute. People who come to Aikido with an intensive Karate/TKD background usually have the most difficulty relaxing, flowing, and moving from the hips/lower body instead of using arm strength and planted feet... moreso than people with no prior MA experience or experience in other sports, for instance. The two arts are based on almost diametrically opposed strategies, as outlined above. Personally, I don't like the aesthetics or strategy/tactics of Karate/TKD, anyway.
Depending upon what you are looking to get out of it, you could probably cross train in something else and get it in a way that might synergize with your Aikido, or at least not interfere. If you want to punch and kick, western boxing is more fluid and mobile - and they teach you to dodge, slip, and move out of the way of strikes (and it doesn't take "5 million years"). If you enjoy the solo form practice, Aikido has Jo kata, and there is always Tai Chi and other chinese arts with perhaps a more Aikido compatible movement style. For 'getting a workout', embarking on a well-designed regimen of resistance training and endurance intervals will bring results much faster and more safely than Karate - in general, one should get in shape prior to doing things like Aikido or Karate, not do them for the sake of getting in shape.