A couple of weeks ago I had a bash around the newly-electrified bits of Glasgow (including Whifflet and Cumbernauld) to see how things were progressing up there. I was pleasantly surprised to see an electric train running from Cumbernauld to Dalmuir via Queen Street low level. However, to reach Queen Street low level, the train must reverse at Springburn. The lines from Springburn to Queen Street high level are not yet electrified (this will be done as part of the EGIP). Construction of the Garngad chord would allow the train to run directly into Queen Street low level (although it would then be unable to pick up or drop off passengers at Springburn, because it would avoid the station completely).
Another electric service to be introduced recently is a train from Ayr to Edinburgh, calling at Glasgow Central. This in reality is a combining of two services, the Ayr-Glasgow and the Glasgow-Edinburgh (via Carstairs) trains. The trains runs to Glasgow from Ayr, where it reverses and then heads to Edinburgh.
A faster Ayr-Edinburgh service using Glasgow Crossrail and the Garngad chord would avoid Glasgow Central completely. Without the Garngad chord, services from Ayr could use the city union line to access the Airdrie-Bathgate line to get to Edinburgh. Diesel trains could theoretically use it in its present state, but electrification is preferred. However, the Garngad chord would give trains the option of running via Falkirk, which is a faster (although less direct) route.