And, of course, there's always the fairly logical outcome of this situation. The Hive Mind comprehends that it is under assault by something within this galaxy that is considerably more dangerous than anything it has previously believed to exist here. So it retreats to outside the galaxy again.

And then it activates everything it has, deploys in a widely dispersed pattern, and hits everywhere at once. The vast bulk of the enemy fleets aren't nearly as dangerous as the Culture, and even the Culture cannot be everywhere, or move from place to place with the speed necessary to fight on anything more than a small number of fronts. Worlds fall to the Tyranid advance by the dozens, and then the hundreds, and then the thousands. And every world that falls is consumed wholesale and it's every inhabitant devoured, before the newly reinforced splinter fleet fragments and heads for the next half dozen of known inhabited worlds (the information obtained by Lictors and other specialist organisms).

The Tyranids might never bring down even a single Culture ship. They don't need to. Because once all the other worlds are gone, the Tyranids turn around again and head back out into the interstellar void, leaving the Culture and whatever they managed to protect directly sitting in the barren wreckage of a galaxy. Because the Hive Mind has the numbers and coordination to fight a unified war on a hundred thousand fronts, and no one else does. There's more to a war than simply who has the biggest guns, after all, and from what I've seen the Culture would consider the total outcome of such a conflict a loss.