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?
You can do it but you should not.
Exodus is a close source wallet, and it's not a good wallet software to use. If you are worrying about risk from a close source wallet like Exodus, you will have a better option, create another wallet by Electrum wallet software, offline, and send your bitcoin from Exodus wallet to your new Electrum wallet.