It's slightly different from 16K tape games though since nearly half of a 16K Spectrum's memory is taken up by the screen, so 16K tape games really only have 9¼K for code, data and variables, and the rest is the screen. A ROM game could have a full 16K of code and game data, use the RAM for variables (16K or 48K) and still have the screen.
And as MAK says, even a 16K cartridge could unpack compressed code or data into RAM before running it. That's how most cartridge consoles from the 16-bit days onwards work, since games were getting bigger far faster than ROMs were coming down in price. The N64 relies on this extensively, which is why you still get 'loading please wait' messages and limited 3D textures from a cartridge game.
Also note that the Interface II turns joystick inputs into keypresses, so won't work with +2A and +3 machines.