There are a few issues here, and it's important to think of them, and deal with them, separately instead of assuming that one determines the outcome of another.
First, there is the issue of whether this company is allowed to collect in Florida. Well, this question can have a few different answers. A lack of Florida licensure may prevent them from taking on accounts from clients in Florida, but may not bar them from collecting from Florida residents. It certainly does not prevent them from hiring an attorney to bring a lawsuit in Florida, regardless of whether or not they are actually legally allowed to do so.
Second, there is the "forum" issue (the matter of whether a Florida court would have jurisdiction or would be a proper venue for this claim). Venue probably isn't an issue because the debtor resides in Florida. Jurisdiction is a bit trickier. If the debt originated in Wisconsin, and the lender is a Wisconsin company, then a Florida state court probably doesn't have jurisdiction over the matter. A federal court wouldn't have jurisdiction either because the amount claimed is too low. But there may be other factors here that would allow for jurisdiction in Florida.
Then there is the statute of limitations issue. Generally, the statute of limitations begins to run when the last payment is made or when a payment arrangement is made. There is alot of confusion over payment agreements and statutes of limitations. Many people think that restarting the clock when an arrangement is made is an illegal re-aging of the debt. It is not, because it is not actually a re-aging. Rather, the payment arrangement creates an entirely new contract, thus restarting the clock.
Finally, assuming that this agency is not allowed to collect in Florida, that jurisdiction is inappropriate, and that the statute of limitations has run out, does any of this prevent them from filing a lawsuit? NO!
These are defenses that could be raised within the context of a lawsuit, but they do not prevent a lawsuit, nor do they prevent the plaintiff from receiving a judgment.