If one was able to find a way to create infinite amounts of latinum that individual could become rich. That is until the amount latinum floating around made all latinum in the alpha quadrant worthless.
They may find another currency, but their economy would be damaged.
It is clear from several episodes that Gold Pressed Latinum replaced Latinum before it. Latinum replaced gold. Even without a physical currency the cultural and economic system of the Ferengi could easily be maintained through a type of Fiat currency - the most important factor being only to "keep score" and accumulate "wealth."
Keep in mind that only a very limited definition of wealth includes physical currency. Property rights are very important to the Ferengi people, and property can be accumulated just as easily as Gold Pressed Latinum.
Even if Gold Pressed Latinum could be replicated it would still maintain a minimal level of value depending on the cost of energy and raw materials required to replicate it.
It is a common misconception that replicators can create matter, they can not. They simply rearrange existing matter into what ever form is desired. Diamonds can be created from carbon. But to create gold (and presumably latinum) requires that you first have gold or latinum to build it from. Very rarely will you ever see anything replicated in Star Trek that is made up of rare or precious materials. All items are also recycled and put back into the various elemental stores aboard ship.
Creating and destroying matter is by far the most energy intensive activity that can be done, and presumably would be avoided at almost any cost.
There's nothing wrong with "speculative questions," and no reason to add a delete tag.
As a really minor note you wouldn't even need to replicate the gold, you'd just need the latinum. The gold is just use to wrap it. In fact if your goal was just to create some type of counterfeit gold pressed latinum bars you could just use a filler material pressed into gold bars of the same size like what happened to Quark in "Who Mourns for Morn"