Nah the BBC have already made statements on this, they will use BritBox more like DVD re-releases, no one will pay for any show twice. BBC co-produce many shows with other companies though, they get a lot of funding to co-produce shows from Netflix for instance, so any majority ITV funded co-produced show does have the chance of ending up on BritBox, but all BBC shows go to iPlayer if they have the licensing ability to do so, for a year under new rules. This is basically for watching >1 year old TV shows as far as BBC content goes unless you're abroad and can't access iPlayer.
Also worth noting any shows that are made for BritBox will be done on a near non-existent budget by modern standards(About x1000 less than say a Netflix shows production cost), and any BBC profits from the service go back into funding more general content production.
The whole point of this service is to stop American re-sellers siphoning all the profits off rebroadcasting British content, which is harmful for our use of the TV license.