I suspect there are those more knowledgeable than me but FWIW:
In theory why not? The Beeb has one and it should 'just' be a matter of power and support circuitry which can be mostly lifted from the Beeb's schematic. I can think of one or two 'gotcha's' off the top of my heard, there may be more:
-Some of the addressing in the Elk is different / more restricted than the Beeb. If the IC has to live at a 'non-standard' address that's going to limit software compatibility
-The 'OS' will need some rewriting in places, possibly return the Beeb code, to be able to drive it. Unless directly banging the metal is the plan
-The Elk handles it's more limited sound via the ULA, I imagine a SN76489 won't just need power & addressing but the whole hog on the output side too
-With the ULA being a single device handling almost everything the Elk does, including sound, I wonder if it's going to be as 'simple' as addressing a new IC or is the ULA going to get in the way, so to speak
I'd certainly be intrigued by the idea of an Elk with a proper sound chip, assuming it was useful. I wonder if far more knowledgeable peeps over on stardot.org would have some more useful thoughts? I do remember that's been some discussion about a replacement / upgraded ULA for the Elk which may shed further light on technicalities.
I hope that helps a bit.