I tried Co-op GMing in 2nd Ed D&D (I think) it was a bit of a disaster really. But then neither of us were really experienced (or particularly good for that matter) at GMing back then. I've since tried a few games rotating GM more recently, which was ok for something fairly knockabout. In that the GM's character was off elsewhere and it worked fine.
In my experience GM characters (and even just accompanying NPCs) are a nightmare to handle whilst GMing. GMs have enough to do to without maintaining a character in the party. All that happens in my experience is that everyone frequently forgets they're there and then occasionally they're remembered, usually just to save someone or move on the plot a bit.
Particularly in Shadowrun, where the party is essentially mercenaries, it's easy to explain an absence of someone for a while. Or alternatively, have them off running a separate part of the mission. Say a distraction, infiltration, hack, sniping cover, overwatch, get-away driver etc. That way if everything goes to hell you can call them in to prevent something like a TPK without it being a huge deal.
Good luck with the co-oping