Yes, grads will be FMGs because they will be getting an Australian degree.
No, it will not be accredited by the LCME because the program is Australian.
The program was set up by the University of Queensland as a route to help American grads get back to the US. To date, N. Americans studying med in Australia have either stayed here, or have been allowed by their schools to complete one or more clinical terms back home before returning once they graduate (the more done back home, the better come residency application time -- all the older graduate med schools here allow this). As post-graduate training spots dry up in Australia with increasing domestic graduates, increasingly N. Americans will have to return home for residency.
The UQ/Ochsner structure is akin to that of the Carib schools, in that students do their first two years outside the US, then all their clinicals in the US. The main diff with the Ochsner program is that it's part of a traditional foreign university, and the first such program in the US. That doesn't mean it's better than the Carib schools, several of which have a very good track record of placing grads, but it's another route for those who don't wish to go to a Caribbean island either due to location or any perceived stigma or because they're not seeking a backup school.
On the other hand, UQ, as its Ochsner program, doesn't teach to the USMLE Step 1. Australian schools teach less basic sciences than American schools, and Ocshner has essentially the same curriculum as UQ (out of necessity -- the program wouldn't have been accredited here as part of UQ if it didn't), so students need to supplement their studies with preparation for the exam. UQ has promised and been organizing tutorials and exam prep help, along with time off to prepare, but I don't know how the specifics are evolving. However, it's at least not an untrialled situation, as Australian grad schools have been placing smaller numbers of N. Americans back home for over a decade.
UQ/Ochsner is also costly (~$50k per year for four years, which is incidentally about what St. George's charges).
I personally think the UQ/Ochsner program was marketing brilliance, and I have (and do) support its creation. Whether it's appropriate for you, however, is a different question. Do your research into all your options, and do what fits you and your goals best.