I don't think you will find that there is much travel from West St Leonards and stations north thereof to Lewes and points west. My wife used to buy a ticket, at Warrior Square valid from Battle to Brighton, as the peak fares undercut those from St Leonards. Despite having thus an option to return to West St Leonards I cannot remember her ever actually doing so.
Years of observation of usage in the area makes me very doubtful that there is any significant round the corner traffic that would be susceptible to being affected by re-opening the Uckfield-Lewes section.
I've no idea where the proposed reopening would fit in the list of national priorities, but feel that (1) it should not have been closed in the first place and (2) would attract a significant all-day, year round traffic, without taking any account of London traffic or diversion opportunities. Projecting the Uckfield service to Lewes/Brighton would mainly help balance the loads along the line. Some passengers from Lewes to Croydon/London might use it but I cannot see how it would be attractive to Brighton area passengers unless the fares were skewed.
The pre-war electrification of the Southern created a rail-mindedness, along the coast, which still persists. 5tph between Brighton and Lewes and 6tph between Brighton and Worthing (4tph plus 2tph changing at Hove) are not run for the fun of it, but because there is considerable traffic offering. Unlike in the London area this does not require the prop of free rail travel for the elderly or massive off-peak stock availability. It does benefit from the growing population being constrained by the South Downs which tightly defines the area available for building, a vibrant student population, less than superb roads, a significant 'grey market' (including yours truly!) and a built and unbuilt environment worth fighting for.
My view is that this re-opening would pass the Scottish-test but, of course, it is in non-metropolitan England.