Unfortunately Edinburgh would need one on the east side of Waverley to support east Coast compatible trains, which would presumably be required to terminate there.
Come to think of it a platform would be needed at Newcastle, and I think it is rather hard to arrange without remodelling the northern end of the station to take up space in the carpark... I assume the trainshed is listed?
And one platform each might be pushing it in times of disruption, two platforms would be far superior in terms of redundancy.
I was thinking predominantly of platforms for HS2 Phase 3 captive train sets, but effectively the planning for 200m/400m compatible sets is the same. At present, of course, the Phase 2 configuration is for two hourly 400m compatible services from Euston to run up the WCML and split at Carstairs. There is no plan, at Phase 2, for compatible sets to run into Scotland from Newcastle; and if they did, they would suffer in comparison with those going down the WCML.
The suggested splitting has aroused a fair amount of ridicule amongst the Scots; but the alternative would be for one 400m service per hour to each of Glasgow and Edinburgh, with a connecting shuttle service between Glasgow and Edinburgh via Carstairs. But that assumes that the Scots are able to build Glasgow-Carstairs-Edinburgh as standalone high speed line in advance of the stately progress of English HS2 north from either Wigan or York. In which case the Haymarket and High Street HSR platforms are going to be built to captive specs anyway.
So the compatible trains north won't be coming into Edinburgh from the East, but from the west stopping at Edinbrugh International Gateway (Gogar to you and me) first. Which is why the platform has to be at Haymarket. In any case Waverley is seriously difficult for access up to buses and trams; while Haymarket is pretty much on the level. The Glasgow-Edinbrugh shuttle, of course, won't be able to share use of the HSR platforms, but can presumably be built to Javelin specs, and so (as a classic compatible) will be able to run through from Waverley to Queen Street along their respective tunnels.
I agree that having only the one platform couild be tricky, and perhaps Glasgow will splash out and build two - as there is certainly space at High Street. Haymarket is trickier. and an extra platform could only be achieved with some demolition. More likely, in case of disruption, the Scots would simply terminate the Edinbugh services at Gogar (where there will certainly be two HSR platforms).
The Newcastle trainshed is listed grade I, and there is no possibility at all of shifting it. I'm inclined to think that a westward-facing Newcastle captive spur could best be provided alongside the Redheugh bridge on the Gateshead side of the river.