BitTorrent the company has been fairly far detached from the protocol and software introduced in 2001. The original client discontinued, µTorrent is proprietary, and launching various services like BitTorrent Sync and Play that really don't have anything to do with the protocol at all... I'm honestly surprised that the company still survives (though this may be why it's being acquired).
Long story short, no, it won't affect you using the protocol and Transmission or what-have-you to download Fedora ISOs.