If Graves, Blasting Through gets assault, does it deal 4 damage or damage with assault might?

Yes — the damage equals its current Might, so Assault is included. Graves is a 4 Might base, so with Assault 3 he'd deal 7 to all enemy units here when the attack trigger resolves (Rule 710: units are evaluated at their current Might, and the ability's value is read at resolution, 359.3.f.4).

Assault is a passive "while I am an attacker, I have +X [M]" (Rule 807.1.c), and the attack trigger resolves during the Combat Showdown while it still holds the Attacker designation — so the bonus is live when the number is read. On defense Assault does nothing (that's Shield's territory), so a defending Graves deals 4 unless something else pumps him.

One note: this damage is from an ability, not combat damage, so combat-damage modifiers don't touch it — and since Graves doesn't deal combat damage, the ability is the only damage he's putting out.