Carb rebuilds are almost always a good idea, what`s a few more bucks and a little time when you are repairing to this extent.
Of course checking the carb boot is a good idea but it is not likely to be the problem. A word to the wise, carefully examine the position or relationship of the boot and clamp to the cylinder and make note of this position for ease of re-assembly. You will also need to remove the round metal piece which will be exposed when you remove the carb so that the boot will collapse and pull through the frame of the saw and you remove the cylinder and boot as an assembly. When it is time to re-assemble, tie a piece of string around the end of the boot to help pull it back through the frame. It`s easier than it probably sounds. Also make note of the torque on the cylinder bolts before you remove them. It`s not awfully high and you should be able to easily remove the bolts with a decent screwdriver type tool. I think the torque spec is 7"lbs just to give you an idea. If you can`t find the spec and want it let me know, I`ll get it, in fact I`ll get the part numbers while I am it.
Russ