Definitely....
My philosophy on training is that if you aren't so sick you can't get out of bed, you should hit the gym and give 100% of whatever you have that day.
I say that because if you wuss out for being "sick" when it's not that bad, you're conditioning yourself to use most any excuse to not train.
A poor day of training (even if it's your best effort) is better than not training at all in my book.
The key to training is always listen to your body. I've had days I felt fine, but got to the gym and it just didn't happen. I blew off training that day just to be safe (don't need an injury because I'm too out of it or not focused). I've had days I didn't feel that great but got an impressive routine done (maybe it was just in comparison to how I felt that it seemed impressive).
That, and for me, when I have a head cold or chest congestion, cardio work does wonders for clearing out everything. The body heat elevation, the high rate of breathing, all of it just seems to help the body get relief for a few hours. Sitting around at home or staying in bed only makes me feel more sick.