I would think so, but I'm not sure this is a rigorous way of looking at it. The more rigorous approach can be described in words by using the block universe approach, where one assumes that the entire history of the black merger can be described in the block universe, via a metric. The metric, then contains the entire history, past and future, of the merger.
From this metric, containing the entire history of the merger, one computes the signal in "space" as a function of "time", in some small region of space-time far away from the black hole. The problem of splitting space-time into space plus time in a small local region has a generally accepted solution, which can be described concisely by saying that the process involves using projection operators to projecting the 4 dimensional space-time into the appropriate subspaces. (This isn't very detailed, but I hope it's sufficient).
This approach doesn't have any simultaneity conventions for it to depend on, at least not until the very end of the process. At the end of the process, one usually imposes the condition that time is orthogonal to space, and that the different spatial directons are also orthogonal.
When one talks about a scenario where "the black holes just touch", my interpretation of this is that one is imposing some specific simultaneity convention, some specific coordinates, to describe the state of the black hole at some "instant in time", so one can single out a specific instant in time "where the event horizons touch".
One might ask - why be so careful about waiting until the end to spit up space-time into space plus time? What's wrong with doing the split earlier? The short answer here is that while the splitting of space-time into space+time in a small local region is well understood, there are some well-known difficulties in doing so over a larger region. Much depends on exactly what characteristics one demands of the split. The particular assumption that's problematical is that there exists a split that is hypersurface orthogonal. This problem arises in, for example, the rotating disk - where no hypersurface orthogonal split can exist. Similar issues and confusions will happen when one tries to describe what one means by "an instant of time" in the binary inspiral. We don't expect a hypersurface-orthogonal split to exist there, either.
Recall that in my description of how we made the local split for the observer a long way from the black hole who was observing the inspiral,, we did impose an orthogonality condition between time and space.
Without a specific answer to this question, of how to single out some specific hypersurface of the inspiral that corresponds to "the instant when the horizons touch", I feel that it is best to be cautious about proceeding further. To really be sure, one would actually have to rigorously define how one was making this split to be able to describe the inspiral in this manner, and do the necessary calculations using the resulting coordinates. The point is that one doesn't have to do this to figure out what the signal at infinity is - one can defer the issue of the splitting until later, and when one does so, the mechanics of how to do the split are generally well accepted.
This brings up the question of how the calculations for the expected signal out of an inspiral were actually done. There are certainly papers in the literature that describe the process, but I can't say I'm familiar with them. I believe developing the numerical codes and ensuring their accuracy and convergence was a very long and challenging process. I would expect, though, that conceptually they used the general framework I outlined earlier, a framework that can be described as a 4-dimensional "block universe" view of the problem, that doesn't single out specific instants of time for the inspiral process, but instead comes up with an abstract mathematical representation that does not depend on such a split.