For a simple electrical design, usually something like a blower motor regulator would be JUST an output from the control panel - and would not have anything to do with the control panel's operation. Could not in any way cause it to not operate.

But with more advanced electrical designs - some systems do fancy "self checks" and might not "boot up" if everything associated is not working/responding to commands.

Thus it is IMPORTANT to look at the wiring diagrams for the SPECIFIC YEAR AND MODEL vehicle to see how the system works - and to mention same when asking questions like the above.