>>>I think I'm going to have to check the thermostat.<<<
Can you be more specific? why?

>>Will the pressure build up and start blowing weak cooling components?<<

Well, of course if the pump is dead (basicaly impossible!)the pressure will
rise. (Heat up = pressure up) Pump are design  to "wear out", they are
"coolant lubricated", when one of the seal/bushing slowly fail, by design,
there is a small openning that let a small stream of coolant out, this is
sign that the pump is going away. If by any bad chance the pump would
completely failed (mechanicaly break), the belt would slip or break, the
alternator light would go on and you would hear a very hissy sound. (belt
slipping). I also don't belive that pump are partially working (giving very
low pressure), mine was cooked (touching the matting surface of the engine
case), still, my engine was cooling fine (with a nice metal to metal sound).
http://www.benplace.com/engine/engine_after1.jpg

Thermostat are also design to break in the open position.

What is your problem? your post is not very clear!

Regards, Ben
http://www.benplace.com/