Damn right he is going to deviate from his clearance. He needs to descend very quickly to the aircraft get into more oxygen and to relieve the strain on the structure in case anything else gives way.
If you are lucky he will have sufficient situational awareness to turn off track and descend into clear airspace but his office is now a howling maelstrom of paper cups and flight publications, so dont count on it.
I would definitely expect him to remember to squawk emergency and I would definitely remind him if I did not see it. If all I get is one shout of 'mayday' I will tag it and get busy trying to make some room.
I would then be telling my watch Supervisor/Sector Chief/anybody to spread the word for everyone to get the hell out of the way and to offload the rest of my traffic cos the emergency aircraft is now the only show in town.