They will definitely use the new duct to provide service.
If it were a like-for-like swop (copper to hybrid FTTP) going overhead, then they would recover the old copper cable, but as j0hn states, it will probably remain in-situ for the time being as the engineer has no need to climb the pole to provide FTTP to you.
Not knowing the geography of your premises, there may be more to removal than meets they eye ??. Engineers use a 'Tetra climbing system' (Google it), and if the criteria can't be met to ensure its use then other options will have to be sought .... such as using the cherry-picker or a scaffolding tower (sufficient access area, dependent with both).
If that fails, I've recently had eyes on a trial going on in OR using mechanical cutters for this sort of thing. Never seen them, but I believe they're a heavy piece of kit therefore requiring two men to use them .... once the cutting head is in place the 2nd man then uses bluetooth to operate the cutters. As I say, these are currently in trial and if you don't live in the trial area (wherever that is ?), it won't be an option.
Hopefully I've covered all scenario's ??.