I took a Brompton on the Airdrie - Edinburgh train last month.
People frequently take cumbersomes on the Queen St - Airdrie section. It might not be popular at rush hour but I've never had any grief and I have occasionally taken a cumbersome or a trailer on there. I fold the trailer but leave the wheels on so it just sits against the wall.
I don't remember putting a cumbersome on at Queen St, I'd usually got it in place at Charing Cross or somewhere further west where the train was quieter.
When I used it for getting to the Mysterious East it was busy in the morning from Bathgate to Waverley. I got one back around 1700 in the afternoon and it wasn't busy.
The Glasgow Queen St to Bellgrove section can be busy if the footballists are playing at Parkhead.
The newer Class 334 trains have a wheel chair area beside the toilet. Bikes can fit in this area but it's not designed for them. The older Class 320s have a sideways flip up seat which fits a bike when flipped. They are at the ends of the 3 car units. I don't think 320s will be running as far as Waverley as they have no facilities, indeed I don't know if they're still running on the line at all now.
http://en.wikipedia.org/wiki/British_Rail_Class_334
http://en.wikipedia.org/wiki/British_Rail_Class_320
And I use Marathon Plus if I absolutely have to be there on time. They're not fast but they will get you there. Looks like the Pashley at least three days a week till the end of June as I have to be back at the nursery with the trailer and on at least one of the days I don't have time for a flat.