These were colour light signals and standard practice would be for them to revert to danger as soon as the train passed onto the track circuit beyond, which in the major termini would be only a few metres after the signal. In which case they would definitely be at danger by the time the released loco got there.
Sometimes a special control was fitted called "last wheel replacement" which keeps the proceed aspect displayed until the whole train has passed it. You can still see this at Derby. However the main reason for installing this at a terminus would be to ensure that a driver propelling a train didn't see a signal revert to danger ahead of him - Derby did and probably still does have many trains propelling to the RTC sidings. However propelling to sidings was an alternative to the loco following the train out, and at the stations where locos followed the trains out last wheel replacement probably wasn't necessary and may even have been forbidden (I'd be interested to know).
Absolutely right regarding the last wheel replacement in Derby station.
Propelling from Derby station to Etches Park was allowed in the 80s as long as there was a guard's brake as the rear or next to rear vehicle. The last wheel replacement was so as the driver, being unable to see the guard as the curvature of the line prevented it, would have the reassurance of a clear signal when his loco reached it. If however there was no rear brake, a shunt engine or run-round was required.
Before that, propelling was universally allowed until a loco-hauled train propelling from platform 2 to Etches Park had the signal put back on it when it failed to move. The route timed out (2 mins) and then a route was cleared for a a 2-car Class 114 (Lincoln) DMU to leave Platform 3 for Nottingham. You can guess what happened next - both trains moved and met in sidelong collision over London Road Junction!
There was also a propelling incident (not in the station but badly affecting it) with a train of brand-new Mk 3 coaches en route (as 5A12 0820 Derby EP - Willesden CS), out of the works being propelled out of Etches Park, running past DY428 at danger and straight through the middle of a Class 7 Tinsley - Severn Tunnel freight passing over London Road Junction on the goods lines.! It didn't do the brand new coaches a lot of good and the regulations were then changed so as DY428 had to be cleared for all propelled movements out of EP towards the good line.
After the mid 80s no propelling was allowed at Derby Station at all - shunt engines were employed to dispose of loco-hauled trains but by this time they were getting much fewer in number as HSTs were being introduced.
At St. Pancras too in those days, all trains were re-engined and the "bank" engine as it was called (the loco at the buffer stops) would follow the train out at a respectful distance. The signals there were "first wheel replacement", i.e. the track circuit controlling that signal started immediately after it and thus the signal would revert to danger immediately it was occupied by the first wheels of the departing train. Thus the the driver of the bank engine would never mistake the platform signal cleared for the train as being for him.