Just what the title ask. Can a Vampire fall unconscious due to physical damage (bashing, lethal or aggravated) without entering torpor, like being hit in the head? What are the rules for it?
You need to be at Incapacitated with enough blood to heal yourself conscious.
When a mortal takes enough health levels of damage to become Incapacitated, they fall unconscious. When a vampire takes that many health levels, they either spend one Vitae to heal themselves to Crippled or, lacking that blood, fall into Torpor. It's possible to lose consciousness during this period of being Incapacitated — Sabbat mass embraces are described this way:
This infamous method consists of collecting a number of victims, Embracing them with the tiniest quantity of blood possible, bashing them over the head with a shovel (to knock them unconscious before they frenzy), and burying them in a mass grave. The newly Embraced Cainites rouse quickly, and they must dig themselves out of the grave to sate their frenzy, often at the expense of the weaker vampires entombed with them.
So there's a period while being Incapacitated where one can "be unconscious" without falling into Torpor. However, there's no equivalent to the "knock on the head" where you're unconscious without having your damage boxes full of damage. (Certain disciplines can do it, but they're exceedingly rare -- Daimonion 2 and Auspex 8)