Yes, I have taken 1 v 0 successes in a melee as a decisive victory.
Fall-back is certainly one of the main reaction options, particularly for cavalry, assuming it is available (not for infantry v cavalry or a unit that cannot fall-back at least 1 BW). I probably wouldn't try the fall-back if the unit falling back had to interpenetrate a unit on 3 DSR, which could be lost if it failed the interpenetration discipline test. I wouldn't try the fall-back if attacking cavalry could cause a problem when they take a momentum move. For infantry, particularly amateurs where I only have a 50% chance of succeeding with the fall-back, I might shoot rather than fall back, particularly if the attacker already had one or two disruptions.
Depending on the size of your table, 3 battalions sounds a bit small for a good game. You can certainly have a successful game with the core list and attacker bonus - 8 or 9 battalions and an artillery battery or two a side, with the C-in-C and 2 sub-commanders. You should be able to keep everything in command. I've not tried a game with each side having only the core list without the attacker bonus. Since that would only have the C-in-C and one sub-commander, it might be harder to keep everything in command. On the other hand, if you just have the core list, with no support brigades, you may find in an attack/defend game that the attacker bonus is a bit too unbalanced.