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No you shouldn't. AV1 and AV2 are both inputs to your TV so whatever outputs i.e. Freeview on AV1 and your games console on AV2 could both output to the TV and to an AV sender - note that you would need an AV sender for each (or one that could switch between them) if you wanted to be able to watch both in another room. You would also need multi-SCART adaptors to split the outputs to go to both the TV and the AV sender.
Just to complicate matters further, your AV2 TV input can also probably output whatever is on AV1 and quite possibly other inputs - you will need to check your TV manual and set it so that your AV sender isn't getting a signal from the TV as well as the games console.