Would you let players exceed wealth by level if they attached RP drawbacks to it?

For example, a nice +1/+2 Greatsword at the start of a level 3 campaign, the paladin took it off the corpse of an enemy commander, having destroyed his own weapon in the melee. Now it's both the symbol of why he was knighted, and a beacon for cutthroats who want to kill him and take the sword back.