I only ran into this issue when my bike sat for about a week or so, long enough (I presume) for the float bowls to empty out. After I got it going again, it usually started pretty quickly the next day.
But I agree: if you don't have a good enough battery, it's possible to run it down long enough with the cranking that you compromise the ignition portion. If you can get it to stumble a bit, then you're probably OK.
Luke M
Used to have a 1979 CB750L, sold it as a parts bike, now riding a slightly modified 1984 VT700C. Network/Field Engineer. Central OH, USA, Earth, Sol System, Milky Way Galaxy, Universe.