Possible, but very unlikely I'm afraid.
Hastings MP was full of herself recently after luring McLoughlin away from his HS2 department of spin to have a look at the problems between Hastings and Ashford. The "outcome" of it all was NR and McLoughlin sounding very positive about juicing Marshlink in CP6 and running Javelins through to Bexhill which in effect gives East Sussex what Kent has had from day one when HS1 opened. I haven't gone into the TSGN proposals - do they mention Marshlink overcrowding issues at all?
The obvious solution as mooted elsewhere on this thread is electrify the two pockets of diesel operation (and may I add - do it properly and also reopen Lewes Uckfield). The overcrowding on the Uckfield line is duplicated on the pitifully inadequate 2 cars that operate the Brighton Ashford service. The Uckfield London Bridge overcrowding problem would never have been predicted just a few years ago - but give people a direct service and modern trains - they'll use it!
So far as Marshlink issues are concerned - the overcrowding is a daily problem now NOW and the recent proposals we have heard, at very best, might see a significant improvement with electrification and 6 car Javelins in SIX years - TEN at the worst, if CP6 sees work commence.
An interim solution may be to just use the two cars on a Hastings Ashford service with a cross platform connection at Hastings off a 4 car 377. But then Southern/TSGN will always sail close to the wind with their rolling stock and not have enough 377s to take up the Brighton Hastings part.
Another solution is to sub let Hastings Ashford to an operator with experience of packing them in.......