By the way, I think having straight up negative coin is fine as long as it is clear how it works (which it wasn't when Armada was first posted, which is why I asked). Interaction with cards like Poor House and Storyteller need to be explained, and whether you're allowed to buy $0 cards while below $0 (the basic rules suggest you can't, but that is economically nonsensical; the rules were written with the idea that going negative would never happen; it's a design principle that Copper can always be bought).
The biggest issue is that it will be confusing to many people who will consider Bridge, Poor House, etc. and assume, not unreasonably, that it means you can never go below $0. Dominion doesn't have a concept of debt in the rules but it does say that you resolve the card as best you can when you play it. If a card tells me to discard and I have nothing left in hand, I just don't discard. It doesn't save the discard until I draw again later (e.g. in the same turn with Golem). So a reasonable interpretation of -$3 is to just pay $3 immediately if possible, but only down to flat broke 0 and ignore it otherwise.
If you don't mind the potential for confusion and clarify all those interactions, I think it's fine to test. A close comparison would be Embassy.