It's serious. As mentioned above, one school actually locked people out last cycle, and people were forced to beg for a reprieve, which seemed to be granted for some and not others. For applicants looking for every conceivable edge, and neurotic about every little typo, it's a good idea to turn secondaries around quickly. Especially anyone who went to the trouble to get their primary verified so early.
Most schools won't lock you out, and 2.5 weeks instead of 1.5 is not going to be the difference between receiving an II or not. But, for the schools who care about intensity of interest, yes, it matters, because you are signaling you have more important things to do, or schools you care more about getting finishing up first, than turning their secondary around quickly. This annoys some offices because they intentionally space out secondaries to manage work flow, and we then screw that up by submitting whenever we feel like it.
Others really don't care, so YMMV. The safe, conservative, SDN move is to turn secondaries around in 2 weeks. It's not a "rule" unless the school explicitly tells you it is.