Guess I'm askin, is something else frozen up, like say,
the starter motor is toast/seized, and the starter relay
is just bouncing trying to start a blocked starter.
Seems less likely than battery down. Whattya think.
I seriously doubt it.
It'll take practically zero effort to try to jump it. It should almost immediately fire if it's just a low battery. I'd say that if it doesn't fire when hooked up to the car battery, don't force it. THEN you could have a bigger issue.
If the starter motor is already toast, you ain't gonna hurt it any more by trying to fire it one more time. Unless, of course, you are worried about being hydrolocked.

In that case, pull the plugs before you try to fire it up. If your bike looks like Old Faithful shootin' gas out of the holes - well, now you've got a whole new set of fun to deal with. If not - I'd bet it's a low battery.