This had to be tried.
So last Monday I caught a SuperVoyager home instead of my usual First TransPennine train and checked out the WiFi (not expecting much because I'd heard on the grapevine that it didn't work well on the Scottish route).
It worked a treat.
Which is great because it means, if I catch a SuperVoyager, I can check and clear e-mails on the way in and on the way home, making the best possible use of the commute.
And, as an added bonus, the SuperVoyagers are a) quieter b) more comfortable and c) bigger therefore you're less likely to find yourself packed in like a sardine, than the First TransPennine trains.
Just a pity you have to pay for WiFi in Standard Class, but hey, you can't have it all :-)