Please understand, I'm not trying to be a smart alec.
(1) I wouldn't be surprised to find (from folks more qualified than I am to answer this) that serious damage would be likely if the converter and inverter were run together. Think feedback loop . . . .
(2) I do not understand why anyone in their right mind would want to do this anyway. It simply makes no sense to even attempt it. Get an adequate (for whatever load you plan to run) generator and don't attempt to create a perpetual motion machine.
(3) Do be aware that substantial loads will suck the life out of your batteries very quickly, unless you happen to have an 18 wheeler full of them at hand. This is WHY they sell generators at the RV store.
May I suggest you simply tell us exactly what you are trying to power and why you need it.