Yes.
Vim-gnome does install gvim, but it also installs a much more feature-filled version of command line vim, including Perl, Python, Ruby, and TCL scripting, system-clipboard, newer patches, etc.
So not only can you continue to use command line vim, you will get a better version of command line vim along with the GUI.
As for SSH editing, I don't believe anything will change for you. I personally have never used vim to edit over SSH, but according to this article, you can edit remote files from directly within gvim with:
:e scp://username@someremotehost/./path/to/file
Even if that doesn't work, your original command line vim will be the same, so (assuming you can edit through SSH now) you could just choose to use command line vim instead.
Also, yes the GUI version is called "gvim", and can be launched either with
gvim
or
vim -g
From :help -g
*-g*
-g Start Vim in GUI mode. See |gui|. For the opposite see |-v|.
{not in Vi}
and from :help gui-start
1. Starting the GUI *gui-start* *E229* *E233*
First you must make sure you actually have a version of Vim with the GUI code
included. You can check this with the ":version" command, it says "with xxx
GUI", where "xxx" is X11-Motif, X11-Athena, Photon, GTK, GTK2, etc., or
"MS-Windows 32 bit GUI version".
How to start the GUI depends on the system used. Mostly you can run the
GUI version of Vim with:
gvim [options] [files...]
The X11 version of Vim can run both in GUI and in non-GUI mode. See
|gui-x11-start|.