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?
Yes, you can recover your Bitcoin in another hot wallet if you have your private key because your private key is the key to your asset saved in the blockchain.
Your coins are not saved in the wallet; they are being saved in the blockchain and not the wallet. That is why you can use your generated private key to assess your asset in any wallet that support the private key, and these wallets are safer than leaving your coins in an exchange where you don't have control over your assets.
Always remember that
not your keys, not your coins.