Yes, the HOA can and will foreclose you out unless you pay them. Unless there is a payment dispute, there is not normally a viable defense. Your best course is to contact them and see what you can work out that will allow you time to pay them, if they will agree to that. If not, unless you pay them in full, they will continue, and of course, costs and fees will continue to accrue, and if you don't pay them, they will sell your house and that will be the end of that.
Since you're not paying your mortgage and are not paying the HOA and aren't represented by counsel, apparently you are living there for free. I hope for your sake you are putting funds aside to have resources to go somewhere and rent, because the "produce the note" thing rarely does more than waste some time. In most cases they DO have the note, and while it entails some effort to get it, at some point they probably will and that will be the end of your defense. I really hate to see people rely on that - in most cases it does not pan out, and meantime they usually lose the ability to raise the other real issues they may have. There are very few of the foreclosure cases I have seen filed in Florida that do not have genuine legal issues, and if they are not raised properly and in the right time, and developed properly via discovery, they are lost.
If your only objective was to play for time, it did do that for you for a while. It may well have been possible to do better, but you would have no way of knowing what issues there may be and what to do with them if they are there. Serious foreclosure defense litigation is often possible, but is specialized and complex. Trying to develop issues like that without qualified counsel is like trying to do your own brain surgery.
Among our foreclosure defense clients are attorneys on their own cases, who are wise enough to recognize that doing this properly entails highly specialized knowledge and experience.