Even if it would work out for them, Tesla is pushing really hard to be a major battery supplier, so they could end up benefitting either way.
It's true, but I don't think it matters. Traditional automakers rely on suppliers for all kinds of parts on cars: headlights, wipers, tires, glass, airbags, and many electronic modules (auto-dimming mirrors, blind-spot radars, etc.). However they do tend to always keep the body/chassis and the drivetrain in-house (sometimes they'll outsource the transmission, like to ZF).
I don't see how this would affect them moving to EVs. Going from ICE to EV means two giant changes: the chassis (to make room for an entirely different layout, esp. because of the batteries), and the drivetrain. Well, the automaker controls both of those. All those other things, like glass, headlights, electronic safety add-ons, etc., are going to be the same either way. You don't need a different blind-spot monitoring system or windshield wipers or tires just because the drivetrain is electric.