If you are just going to slip a new gasket in you can leave the EGR connected...at least I'm 90% sure you'll have the room (I did it with my EGR connected headers, which fitment-wise I don't think are much different than manifolds as far as gaskets/connections go)...just be careful with it.
If your gaskets are the felpro type that have the end bolts cut out on the bottom you can probably leave the two end bolts in a few threads to retain some stability and not put all the weight on the EGR hookup. This also helps getting the holes lined up again as well...which I'm sure you've found doing other manifold gaskets.
If you do have broken bolts you'll probably need to disconnect the EGR if you want to extract them. But if you only have one or two broken, and you can get the rest of the bolts out, double gasket it and tighten down...it should seal up. I was able to seal the driver side of my 9c1 with two felpro gaskets...even with the back two bolts broken off. Not the ideal situation but it'll work till you have the time to extract, throw on new heads, etc.
Hope this helps!