No it doesn’t require, you can keep the licenses on the Soft e-licenser.
But you can move that license from soft e-licenser to the USB e-Licenser if you want to. Once moved to USB e-licenser it cannot be moved back to the soft e-licenser
I have my Elements license kept on the USB e-Licenser as I switch between machines in my studio & home. It’s very convenient for me that way.
No, your computer does not need a permanent internet connection. Only for: “installer download, license activation, account sign up and product registration”.