Expansion will still redshift the light from these galaxies.
The universal expansion, at least by my understanding, isn't so much a force that pushes these galaxies further apart, but instead creates additional space everywhere, constantly. This includes the space between the galaxies that are approaching one another.
The light travelling from one galaxy to another will be affected by this expansion, since the space that light and matter occupy is also expanding. The result is that light "stretches" as it travels, lengthening its wavelength, because the space between one wave's crest and the next is expanding. Since that light continues to travel at a constant speed, these crests will never speed up or slow down to "catch up" with their original wavelength, so the lightwave gets stretched into a longer wavelength with lower energy - that is, it gets redshifted.
The light will still be blue-shifted by the galaxies' movement toward one another, but the Universe's expansion will not push them together faster. Rather, the Universe's expansion will universally (heh) increase the distance between all points in space, including the space between those galaxies. This expansion rate may not stop these galaxies from reaching each other, but it will always serve to increase the distance that they must travel to do so. Because of this, the Universe's expansion will always redshift light, just to a greater or lower degree based on initial distance.
For further clarification, the fact that there is a larger amount of expansion happening "behind" these galaxies has no effect on the expansion of the space between these galaxies. It's not so much a force that pushes all matter away from each other, but the literal creation of more space at all points in space all the time.
Creation of vs expansion of space
Now, there seems to be semantical ambiguity on this subject (or I may simply have an insufficient understanding of the subject - a very likely scenario) concerning the idea of dark energy as a force. Many interpret it (I think) as being a force that pushes matter away from other matter, but I don't think that's what it is. From my understanding, it seems more like a force that pushes space itself away from the surrounding space.
That is, if you were to somehow identify two "adjacent" points in space, their dark energy would push them away from each other. This of course means that those imaginary adjacent points are no longer adjacent, as there is now space between them. We can now identify new points in space between the two formerly adjacent points (note that in practicality, it is impossible for two points to be adjacent in this sense, as we can always divide the space between them further. This example is just a thought experiment).
Following this thought experiment, we find that, counterintuitively, this dark energy remains at a constant density. That is to say, these points are pushing the surrounding space away at the same rate as before, in spite of now being more spread out, and the "new" points between them are also now pushing the space surrounding them away at the same rate. Now, if the density of dark energy remains constant while the space it occupies is expanding, that can only mean that there is now more dark energy between the two original points than there was before.
This is why I like to say that space is "created" rather than simply expanded. It makes it easier for me to conceptualize. If space is thought of as the thing that creates dark energy (whatever it is), and that energy doesn't lose its density when space expands, then it makes sense to me to say that there is now more space there than there was before. To be honest though, I don't actually know what terminology is primarily used among those who regularly study this, just that this way of thinking makes it easier for me to conceptualize.
Disclosure: I am not an expert or even particularly knowledgeable on this subject. If I have made mistakes here, others should feel free to offer corrections. My answer is based on my own understanding gained from my own limited studies of this subject, and I won't pretend to even begin to understand the mathematics behind any of it.
