No. They run down the East Coast.
Virgin East Coast trains run between London Kings Cross to Edinburgh and a small number of services a day go onwards to Inverness, Glasgow Central, Stirling and Aberdeen. If you wanted to go to Glasgow all the way on a VEC train you'd need to go Aberdeen to Edinburgh Haymarket and then change to the Glasgow Central train which is a rather convoluted route, or change at Dundee onto a Scotrail service for a more direct option. But given there's a lot more Scotrail services run direct from Aberdeen to Glasgow it would make more sense to book whichever times and fares suit you best!