Well flying the 737 my take on your question is your commanded engine RPM tends to increase as you go higher till it reaches a max value.. generally reaches about 99-100%(104% being the max).
And yes you fly a const IAS till your mach no. catches up with you either way you keep seeing your TAS increase. finally at cruise of 350-400 you will be doing an approx IAS of 240, mach of .77 and TAS of around 450.
The difference between the warrior and the NG here is that the NG engines should be rev'ed to higher RPM only when the air gets rare enough otherwise under sea level density setting a climb thrust of 100% may not be good for the engines.