Could the loco siding at Piccadilly be used to hold a train between duties to free up a platform?
If I'm thinking about the road you mean, in today's world
stabling in there would never be agreed to, unless it was only for a very short period when the driver stayed with the train,
essentially a shunt move to clear a platform temporarily, and could change ends without having to decamp. It's right in the middle of other running lines, and doubt there is any agreed walking route to/from the station platforms as this would mean crossing other roads. As you say, sometimes 'training' is undertaken in units that lay over for a few hours as well.
Somewhere like London's Waterloo is different, whereby there were two (now one) stabling siding just outside the station, but they (it) are away to one side of the running lines, with a walking route that is via the streets below, so far more user friendly for both stabling (and if needs be, limited training purposes).
BOLD edited:
looking at Google street view there is a view from the end of p4/5 looking outwards, and the rails of the points leading in to the loco siding appear to be shiny, so looks like something had been in/out of there, but the image is dated 2018.