No, it cannot. An Emacs "frame" is a separate editor window, managed by the window manager. Different Emacs frames running the same Emacs session talk to each other--they share the buffer list, etc. Within the Emacs "frame" you can have split "windows".
One Vim session can live only in one window that is managed by the system window manager. You cannot have multiple windows that talk to each other. You can split a single window manager window using ":split" and the like. Vim calls these "windows". You can have multiple tab pages, each of which holding multiple Vim windows, but all these tab pages must reside in a single system window-manager window.
Vim has a help file somewhere saying that Bram Moolenaar knows this is a problem and it's on the todo list.
You can also run Emacs as a daemon, and connect to it from both graphical and tty sessions. So you could ssh into your desktop and (with emacsclient), work with the same instance running on your X desktop.
I did this back in college with XEmacs (90's). I'd leave gnus running at school and open a new frame from home to check mail and news. (You can use this to have two people editing at once too, but you have to avoid avoid opening a minibuffer.)
I was curious so i just tested this to see if it did. It does not. Yes you can have multiple tabs and splits, but in emacs each frame shares the same buffer list as well.