Can I attach NX to an existing X session?

Short answer : Yes.

Longer answer : This update added support for "shadowing", which allows exactly what you are asking for.

I'm not sure if this also exists in the FreeNX server, or the NeatX version.

[Edit: Updated from answer being "no", as there is "shadowing" support in NX now. So this "yes" depends on which version of NX is being used...]

You can now, simply select 'Shadow' in the Desktop dropdown in the client configuration.

Note that it doesn't play well with compositing. If you have to connect to a composited window do this:

Click System, Resize the NX window to get the screen to update, Preferences, Resize Appearance Resize Visual Effects Resize None.

Then it should work. Actually I also just discovered if you go to 'Settings' in the connection config window there is a 'Disable Composite extension' option. That might have the same effect.

It also seems to behave weirdly with dual screen (TwinView).