I have Lucid running pretty stable out of box on my dual core 3.0Ghz Pentium with 1GB of ram, so would it be pushing it to throw Gnome 3 on there?
I have tried searching the Gnome.org web site to find an answer. I have tried a web search based on Gnome 3 requirements. I am surprised at the number of times that this or a similar question has been asked on the forums of various Linux distributions and the same answer is always given. It is a quote from this page:
So, the answer from the official source is "you need a computer built in the last 4 to 5 years and to get the Gnome 3 experience you need hardware acceleration." And that means a video card capable of doing accelerated graphics.
Personally, I would not call that quote a proper specification of hardware requirements for running Gnome 3. But there you are.
In your case if you do not intend to fit a video adapter then you will not be running gnome shell or any other user interface. And that is fine. So, the "hardware acceleration" requirement is not appropriate.
My machine is four years old and it has a slightly lower specification than your machine and it is running Gnome 3 with Ubuntu Unity both in 11.10 and 12.04 development branch in a more than adequate way.
But for completeness of answer I repeat my comment that the video card is the key component for running the User Interface on a Gnome 3 desktop environment be it Unity, or Gnome 3 shell. And a video card with anything less 512GB memory will give a disappointing performance unless used in fall-back mode.
I have found the release notes for 11.10 Oneiric Ocelot which is the first Ubuntu to be built on the Gnome 3 desktop environment.
The minimum memory for the desktop is 384MB. But this comment might be more applicable for you:
Again for completeness I add this link:
If the video card is capable of doing this it is capable of running Unity and I would guess that it is also capable of running Gnome 3 shell:
OpenGL Version required by Unity
Unity requires OpenGL 1.4 of higher. Because of the decoupling between Opengl versions and the first implementation of new extensions by hardware vendors, just having OpenGL 1.4 is not enough. The system must also have support for a number of OpenGL extensions.
There might significant changes on user experience between that version and the latest one (3.2 or something like that). I don't know any backports of Gnome Shell 3.2 for lucid.
The absolute simplest answer:
It's not exactly just Gnome 3, but unity AFAIK is based on Gnome 3. If you can run one well from live, you should be able to run the other.