Looking at the wider picture, about 20 incoming services to Inverness from the south were cancelled this afternoon (including the sleeper and the Chieftan), and consequently, so were all the returning services going south. Even if the line is physically clear in the morning, there doesn't appear to be any trains in Inverness to operate any of the ScotRail services to Edinburgh (unless they magically run overnight with 24hour crews!).
So my conclusion, in the absence of local staff to confirm, is that it is very unlikely that you'll be able to travel at that time. There hould be station staff to ask about other services, which usually continue throughout the morning southbound at about 10 minutes before each hour.