That carburetor is a Walbro MDC. The MAC140 can be fitted with either that carburetor or a Zama - I suspect you have the better of the two.
If by the throttle switch you mean the engine stop switch (kill switch), its only function is to stop the engine when you push it. Hence you will not hurt the engine by running it without it connected, but you have to give thought to how you will stop the engine, either because you want to or because you suddenly need to. In old chainsaws like that one there is nearly always a choke control, and you can stop the engine by operating it. If it is a "primer-only" carburetor, with no choke, that won't work and you need another way to stop the engine. In my opinion is it much better to run the saw with no bar or chain, for your purposes, and it won't hurt the saw to do this for a brief test.
If you find that your engine runs and you want to put the saw back into operation, the original kill switch can be replaced by an ordinary on/off toggle switch, placed in a convenient location, with one side of it grounded and the other side connected to the kill wire that should run to the original red switch. Because many cheap chainsaws have kill switches almost as bad as yours, this is a common modification.
