From what i've read, there were about 6x sets of 379s out on LST - SSD duties today.
So, you have a large chance of getting one, they normally run every 15 minutes.
As I understand it, the additional fast service is a proposal for the big December timetable change- which is also when (with all 30 delivered) some of the Cambridge peak services are due to go 379. The Stansted-Stratfords are also due to be cut back to Bishops Stortford and there's a proposal to run an Ely-Stansted, possibly all-stops, service. Nothing is confirmed yet (unless theplanner knows better).
379's are currently running all the Liverpool st-stanstead airports' as eight car sets