Yes and no.
The Browning BDA uses a heel clip type catch, and CAN use Sig P220 mags, IF they do not have a bumper pad on the magazine base.
Later model P220s (P220 American the one with the push button mag catch) CANNOT use older Sig/Browning BDA mags, because the older mags do not have a notch for the newer gun's catch to lock into.
I have a BDA (bought new in 1980) and have several Sig P220 mags, (American type) that a friend gave me. They work just fine. They just have an extra hole in the mag body that the older mags don't have.