If we knew the answer ahead of time, there would be no point in doing the experiment.
One can easily argue that Mammoths ought to be able to survive - they survived periods with climates similar to our current one and there are a lot fewer paleolithic hunters running about now. But we won't really know unless we try.
Poachers aren't part of the natural environment. When people say "survive in the wild" they are typically referring to the case where the species' and its natural habitat are largely left alone by modern civilization. Any species could be wiped out if humans tried to do so, even humans.
Anyways, in this scenario we have the means of producing mammoths at will, so why would there be a market for mammoth poaching? If people do kill a mammoth, just add another mammoth. Technology works.
One can easily argue that Mammoths ought to be able to survive - they survived periods with climates similar to our current one and there are a lot fewer paleolithic hunters running about now. But we won't really know unless we try.