To be honest I'm not entirely sure. I don't mean to sound glib or anything when I say this, but that would have literally changed everything. The legal precedents that we have now to apply and answer that question would have been almost certainly different.

But let's say, for the sake of argument, that someone found a long lost version of the constitution, constructed in a follow-up constitutional convention that has been up-till-now lost to history. (Come to think of it, that wouldn't be a bad novel premise-- that could get interesting!). And let's say that it had your provision in there. There are a couple of ways that the courts could interpret any subsequent appropriations legislation. The strictly literalist interpretation would be that the federal government simply isn't allowed to buy fish. So no checks could be cut for a bulk purchases of tuna, or something. Another way of interpreting it means that the government cannot subsidize certain maritime industries because treasury money would effectively be purchasing fish. And some can try to draw out the links in the chain ad absurdum. Which some have argued has been the case with certain court cases pertaining to marijuana-- that they were just looking down the chain until they found something that possibly fell under their jurisdiction.

In terms of changing the ultimate conclusion of my answer: It could. Since there was now an explicit prohibition on using treasury funds for the purchase of fish, any congressional legislation that tried to do that would violate the constitution. But for it to have become law, both congress and the president would have been acting in official sense and probably couldn't be sued. At this point, state governments could sue the administration if they tried to enforce this law, which would bring the matter before the courts.

Let's say that the president said no but congress overrode his veto. State governments could still sue if the executive branch attempted to enforce the law. If the president elects to not enforce the law, then we're actually in the same position that we were back in 2014 when Congress tried to sue the president for refusing to execute legislation (vis-a-vis the affordable care act debacle).