The very short answer is no, because no “green screen” standard is compatible with VGA (which is where 640×480 was introduced). The slightly longer answer is yes, but only in a very small number of situations.
The important aspect here is the signal sent from whatever system is driving the display, to the display. Early display adapters (apart from those intended for use with TVs) tended to use digital signals: MDA, CGA, Hercules, EGA and others. VGA and onwards (including non-VGA workstation displays) switched to analog signals, until the advent of DVI-D. Digital here means TTL: on/off only. Early digital monitors tended to be fixed frequency, or at best support a fixed set of discrete frequencies (EGA and VGA monitors).
MDA and Hercules were designed for a resolution of 720×350, with frequencies of 18,432 Hz (horizontal) and 50 Hz (vertical), and used six pins in a nine-pin connector: two ground pins, horizontal and vertical sync, intensity and video (which were combined to provide up to four display intensities, although not all monitors supported the video signal). MDA was text-only, but that doesn’t matter as far as the monitor is concerned.
CGA introduced colour with resolutions up to 640×200, frequencies of 15.75 kHz (horizontal) and 60 Hz (vertical — it was designed to also drive NTSC displays); it used the three available pins from MDA to send red, green and blue signals (remember, just on/off) and dropped the video signal.
EGA moved up to 640×350, with two frequencies: 15.75 kHz horizontal (for backwards compatibility with CGA) or 21.8 kHz horizontal, and 60 Hz vertical. It used the same RGB pins as CGA, and repurposed one ground and the intensity and video signals for RGB intensity (for 64 colours altogether). The new pins are only used for EGA-specific modes.
All the above used the same connector, and the signals are similar enough that you could build adapters. In fact, many EGA cards had jumpers that could be used to configure them to produce an MDA-compatible signal; CGA modes on EGA cards are compatible with CGA monitors. Thus you can use an EGA system with nearly any digital monitor (although the monitor used would limit the available modes, and connecting an EGA system to a CGA monitor which actually connected the repurposed ground pin could destroy the graphics adapter). Some (most?) EGA monitors such as the IBM 5154 were backwards-compatible with CGA. But the 50 Hz frequency of the MDA/Hercules signals would probably mean that colour displays (expecting 60 Hz) wouldn’t work with them.
Going back to your question, all this means that you could use an EGA system with a green-screen monitor, if the EGA system can be reconfigured for MDA-compatible output. A CGA system can only be used with a colour monitor (CGA obviously, EGA if the monitor supports it), or with a television. A monochrome system (MDA or Hercules) can only be used with a monochrome monitor.
VGA is a completely different story, with different connectors and different signals (although as Ken Gober points out, converting the signals isn’t too hard — after all, they’re still h/v sync based with RGB signals). There were “monochrome” VGA monitors (“paper-white”), but they still used VGA signals.
(Nit-picking a little, early monitors weren’t 14” in diagonal; a typical size was 12”.)