If I have a bitcoin wallet on say Exodus, but something happens to the people that make Exodus, could I upload the 12 word private key on a different bitcoin hot wallet such as electrum and get my coins back?
I noticed no one corrected you yet that it is not called 12 word private key,, it is called 12 word seed phrase. The seed phrase is the one that can generate the private key and other necessary information like your addresses.
Also just like others have told you, Exodus is a close source wallet, it is better you send the coin from Exodus to an address that Electrum wallet generates for you.