The stock would need to be made available for it even if Gospel Oak to Barking stock did not become available (and considereing they are 2-car sets with no corridor sections they do not seem ideal for long formations such as 10-car).
Also Uckfield already has 10+2/3 carriages available per off-peak service while the Marshlink only has 3 (and 2 if the off-peak frequency between Hastings and Ashford were increased to 2tph as the route specification document predicts). The fact that Uckfield stock is used less intensly (since far more stock is used in the peak relative to the off-peak) might weaken the business case for supplying significantly more stock to reduce peak overcrowding (a shuttle service to Oxted during the peak replacing some peak London-Uckfield services [still keeping at least 1tph direct between London and Uckfield] would mean that far less diesel stock would be required to meet demand and that electric stock could be used to increase the capacity of the route north of Oxted).
A shuttle to Oxted is unlikely to work and is something that Southern have been seeking to avoid with the Thameslink works at London Bridge. All the peak services from Uckfield are full and standing room only once they leave Edenbridge and some are full before they get there. You'd then be terminating them at Oxted, however most passengers would actually change at Hurst Green to increase their chances of getting a seat so you'd have 6 cars of passengers spilling round the platform at Hurst Green, They'll take time to unload off the diesels, and load back on to the electrics.
However its worse than that because of course commuters remember the days of changing on the way to London and it lead to huge delays as connections often cancelled or running late. Indeed 2 of the peak trains back from London run as a shuttle from Oxted to Uckfield and they are relatively quiet, and fairly frequently the shuttle has to leave before the connection from East Croydon arrives.
Of course it would help if the trains were more intensively used in the off peak but there are problems there. Firstly potential customers dont realise how good the service is these days, they still remember the dire days before Southern took over, secondly they cant come back in the peak hours as the trains are too busy, thirdly they dont trust the last train to run without being a bus as that happens fairly frequently.
Mind you the solution might be to put the transferred stock on the Marshlink and then moving all the Class 171s to Uckfield.