... If the pitots are blocked, this is not a "real" speed change, correct?
Sorry, not correct. Pitot tube data is reality in regard to relative wind velocity flowing past the lifting surfaces. The pitot tubes provide the only indicated air speed data the flight instrumentation software and the pilots had, aside from seat of the pants feel and intuition.
If the pitots are blocked and trapping pressure, a climb should result in an increase in indicated speed as static pressure drops. Correct? (That is not apparently what happened).
Ice blocking or clogging pitot tubes is not likely to "trap" dynamic pressure, which is (1/2)*air density*(relative wind velocity)^2. Instead, ice clogging the tube will tend to shelter the pressure transducer from dynamic pressure. Less dynamic pressure = slower indicated airspeed.
Pitot-Static (Prandtl) Tube
So NO, a climb will not result in a increase in IAS in the pitot tube scenario you describe.
...
The transcript which has been released is probably incomplete, as a couple of commenters here have already pointed out. I'll bet those three pilots did a lot more talking on their way down.