I would look into signing McGee, but only for a 2-year contract. The Celtics could offer him the pro-rated remainder of their MLE, which would be approximately $1.38 million. They could then give him a raise next year and pay him about $1.45 million. The minimum salary for someone with McGee's experience next year is $1.36 million, so you'd be paying him a whopping $90k more than that next year. If he works out, he's a bargain. If he doesn't, he's really easy to move on from. This would essentially be a 2-year, $2.8 million offer.
Teams who don't have cap space or exceptions left can only sign him to the pro-rated minimum, which is about $300k at this point. Accordingly, McGee would need to make $2.5 million in free agency to make up the difference with the offer the Celtics could give him, which isn't impossible, but isn't guaranteed either.
It's not like Shavlik Randolph or Luigi Datome are doing much on the roster anyway. I don't think McGee is great shakes, but I'd rather have him than either of those two, especially with the opportunity to give him a low-cost look next year.