Not so dumb... and the answer is "yes" to the first question and "no" to the
second. The ECU has learned a lot about how your engine expects to run and
will complain with a "check engine" light over things more trivial than the
disconnection of sensors. Eventually it gets tired of whining - that is, it
learns how to operate the engine again - and turns off the light. The
interval is typically specified as a certain number of warm-up intervals,
but may include specs for number of times the engine is started and the
number of minutes elapsed.
I had to have my '93 Chevy work truck tuned up in a distant town, and it lit
the "check engine" light the rest of the day.
Mike