From what I've seen, lots of people have no problem at all mentioning their "non $DAYJOB" stuff on their LinkedIn profiles. Out of my contacts, I see plenty who list a dayjob and also list themselves as the owner/founder/president of a startup, or a consulting company, or some other "side" business.
I actually do that myself... my current $DAYJOB is listed right alongside my startup project. I really don't see it being a problem. <shrug />