The only problem with leaping from such old inferior rolling stock to new high tech state of the art accelerating stock is the timings.
When 387s replaced turbos the acceleration and 100mph instead of 90 meant the new trains gained so much time they loitered (and still do) at every station for up to 3 minutes sometimes.
The timings and entire diagrams for that matter, will need to be reconfigured, and if they only wait for a timetable recast that could mean irritating waiting at platforms in a Stadler that is timed to a class 37.
It is well documented in other parts of the forum that the GWR timetable is due for reworking now that there are enough Class 800's and 387's in service. The new faster timetable is planned for December 2019. In the meantime, early running by the new trains continues.
I imagine a similar thing will occur in Anglia. During a period of transition where new and older trains are running together on the same tracks, it is unlikely the timetable will change. And yes - unless the newer trains start catching up the older ones in front, there is the chance that any superior performance gains will see them running earlier than if in the hands of older trains.
I would hope the newer trains would replace Class 317's, 321's and 315's first, leaving the 360's and 379's to soldier on until the end.
I guess it could be possible to introduce a faster timetable with the 360's and 379's around because they are pretty good performers.
Probably unlikely we will see a new faster timetable for 18 to 24 months yet.
The crucial core from Liverpool Street to Shenfield requires most trains to be performing at the same level - as the headways are quite tight.
If the Class 800's in diesel mode are an indicator of what to expect, i could imagine the FLIRT units in diesel mode to be pretty sprightly at the lower end of the speed range - say 0-30mph, but above that I would guess a pair of 37's on full power with a 3-coach load would power away...but we shall see!