Yes, the Received Pronunciation (RP) trainer will teach you the complete sounds of Received Pronunciation. It will ALSO teach you to hear those sounds using minimal pairs within RP and also between RP and General American, but it's not necessary for you to be extremely familiar with General American in order to benefit from those minimal pairs. They'll just be yet another source of sounds to hear and test yourself with.
Note: As of September 12th 2019, we no longer provide official support for our Anki based pronunciation trainers and word lists. You are more than welcome to still purchase and use them, but the support we are able to offer for these products is limited. For supported languages, these materials are already built into the Fluent Forever app.