As far as the catalytic converter goes, I think the danger would be if
you pushed and/or towed and/or rolled downhill for several seconds (or
more) with the engine turning over but not firing... for example, if you
had an ignition system failure.  You'd dump a lot of raw gas out the
exhaust pipe which indeed could make life a bit toasty for Mr.
Converter.

Other than that I can't see what the problem would be, either... I've
bump-started my van a couple of times without apparent harm.  If a
modern FI engine doesn't start within a few seconds in *any* kind of
starting procedure, there's almost always a problem of one sort or
another somewhere.  If the problem is such as to send unburned or
partially burned fuel out the exhaust (cylinder not firing, mixture way
too rich, etc) then the converter is in danger no matter what.

Ed
'84 plain-jane