There should not be, as the two services are completely separate physical connections to the premises.
However a number of people have had issues where the installer has cut the existing FTTC copper cable and used it to pull in the new fibre service where the route involves an overhead connection across a road or an underground connection through a tight duct. Just make sure on the day the installer is made aware that the new connection is an additional, not replacement, one.
Which of course, doesn't matter if the FTTC service isn't being used. It's nice to have a dual redundant service though: I kept FTTC for a while after getting FTTP.
Check your T&Cs and make sure to diarise the day you need to call your FTTC provider to give termination notice: if you're not migrating to another provider, but ceasing, then they may insist on (say) 30 days notice even when you're out of contract. So give notice before end of contract, choosing a cessation date one day past the contract period.
Also beware that some service providers charge a cease fee for lines which are not migrated to another service provider. This is a cost raised onto them and they may choose to pass it on to you. (There was talk about Openreach getting rid of this charge, but I'm not sure if BTW still charge it)