If a Champion conquers a location with no monsters, would it be considered dealing excess damage in respect to something like the effect of "Vi, Piltover Enforcer"?

No. Conquering a battlefield with no enemy units doesn't assign any damage, so there's no excess damage for Piltover Enforcer.

Excess damage only exists as a concept during the Combat Damage Step — it's the damage you assign to an enemy unit beyond the lethal amount needed to kill it (Rules 465.2.c.3–4). That step only happens when both attackers and defenders are present (Rule 465.1). Moving to a monster-free location is a Non-Combat Showdown: there's no combat, no damage assignment, and no combat cleanup.

So when your Champion conquers an empty battlefield, Piltover Enforcer's "if you assigned 3 or more excess damage" condition is simply not met — you haven't assigned damage to anything at all. (Rule 465.1, 460.2.c)