Can an object grow past the schwarzschild radius?
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TL;DR – no matter that we know of can stably exist at a stage where it’s on the threshold of becoming a black hole, so the “just before” picture isn’t one we think is possible. Black hole densities are achieved during ongoing collapses that, as far as we known, have no mechanism to stop them. This is why we think it goes down to a singularity, but of course we don’t really have any way of knowing – there could be some sort of exotic particle sphere of finite size in there.
To explain: your scenario doesn’t work as stellar material isn’t stable at anything remotely close to those sorts of densities. A typical neutron star – *way* denser than a normal star – of 1.5-1.8 solar masses has a radius of about 10-15 km. The Schwarzschild radius of a 1.8 solar mass object is about 5 km – much smaller than even this densest known stable macroscopic form of matter. We think neutron stars behave weirdly – they may even get smaller as they get heavier – and aren’t stable over a very wide range of masses. We think that when two merge, they collapse into a black hole. But if we ignore that and assert that they could grow to something like 2.5 times their usual radius, at the same density, then yes they would at some point become, according to the outside world, a black hole with an event horizon past their surface.
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