Yes it will work. I actually tried by pulling mnemonic phrase out from the MEWconnect and tried connecting with MEW online and it worked. I haven't tried with other wallets but I am sure it would work in most of them.

But if you fear that MEW at one point would disappear then just download the MEW page. There is a User Guide about downloading and running MEW offline here: https://kb.myetherwallet.com/posts/offline/using-mew-offline/