Only if they're using RFC 6238 TOTP, and not some weird 2fa app. It's ironic you mention authy because they have their own weird TOTP scheme, along with push notification based approval system.
But yeah, things can get messy depending on the specifics, but not installing random apps on your personal phone seems like a pretty reasonable line to make.
I only mentioned Authy cause it was my go-to for 2fa before they got acquired