The manual for my 02 Protege5 says to remove the IAC valve that you need to remove the throttle body. To remove the throttle body it says you need to drain the engine coolant. I want to take off the IAC valve to give a good cleaning, see if it fixes my idling issues. Do I really need go through taking off the throttle body and emptying the coolant?

 

No.
There is a cooling (really TB heating) passage with in/out coolant hoses.

Plug each hose with a golf tee or whatever and the drainage should be minimal.

These are above the rad cap (or close to it) so keep the cap on.

When done - consider buying a connector and 'bypassing' the coolant tho the TB.
99% of the time you don't hot fluid heating the TB and preventing icing. This will keep the incoming air just awee bit cooler - better for perofrmance. Measurable? Probably not - but 'a lot of little' adds up some...