This does work.

However, a better way would be to have the G3D import/export scripts installed in your native Linux blender (which you can get from the Ubuntu repos, blender that is, not the scripts!) - is that the
other way to use blender with full G3D exporting and importing in Linux?
But this will issue an error (at least in my machine). I got the following error from blender:
Compiled with Python version 2.5.4.
Checking for installed Python... got it!
Traceback (most recent call last):
File "<string>", line 1, in <module>
File "/home/$USER/.blender/scripts/g3d_support.py", line 267
SyntaxError: Non-ASCII character '\xb4' in file /home/$USER/.blender/scripts/g3d_support.py on line 267, but no encoding declared; see http://www.python.org/peps/pep-0263.html for details
The link included in the error message tells you why - check section "Defining the Encoding" and scroll down to the paragraph begining with "To aid with platforms such as Windows". You will see the UTF-8 signature '\xef\xbb\xbf' will be interpreted as 'utf-8'. '\xb4' however will not.
But it's sooooo easy to fix that! I checked line 267 in file /home/$USER/.blender/scripts/g3d_support.py - there was an unrecognized character, in a comment! It's in a comment, so you can safely change it, and so I did.

So, in brief, a better method would be:
1. Install blender from Synaptic (or whatever package manager you use) - Wine NOT needed at all.
2. Install 7zip according to Archmage's STEP 2 instructions.
3. Download the Blender.7z archive referred by Archmage in his STEP 3, and extract it anywhere you want.
4. Copy the G3D scripts to the correct place:
cp -v <where you extracted Blender.7z to>/Blender/.blender/scripts/g3d* ~/.blender/scripts
5. Edit /home/$USER/.blender/scripts/g3d_support.py and at line 267 replace the weird character you see in the comment (after the # character) with a single quote (
' ) 'cause that's really what it's supposed to be!
6. Run blender (the native Linux version), go to the Scripts window, open the Scripts menu and click "Update Menu". Installation done!
The Imp/Export tool is in menu "Wizzards". There are also two G3D export formats added to the "Export" menu - I have not checked if these will need some fixing though, but the wizzard loads G3D files easy.

Enjoy.

EDIT: Oh, you can safely remove the "Blender" folder (where Blender.7z was extracted to) after you copied the g3d scripts to your ~/.blender/scripts folder.