1. If the heater isn't running does the coolant flow through the core?

yes

2. Anyone had to switch one out in one of these trucks before? How big of a pain is it? I haven't had a chance to go look at a manual yet.

eh, book time is like 8 hours I believe, and you have to remove the whole dash (at least for 95 I did). If you cut it out of the heater box assembly (I know it sounds barbaric, but on some vehicles you can pull it off and not really hurt anything once you glue it back into the heater box....) if might be just an hour