I would say no, you can only choose the action (at all) if you are currently wealthiest.
In fact, see page 3 of the rules:
rule book wrote:
The final Round introduces the “Renovation” Action tile, which you may only choose if, on your turn, you have more Gold than your opponent. If you are tied on Gold, neither of you may choose the tile, until one of you gains more Gold. (The depicted Gold nuggets on the Action board below the space remind you of that prior to the final Round.)