<p>Can VBA code instantiate and use .NET objects? The specific class I'm interested in is System.IO.Compression.GZipStream.</p>

<p><strong>For Info</strong> GAC is the .NET Global Assembly Cache</p>

VBA can make use of any .NET objects that are exposed to COM. I don't know if GZipStream is or not, but I would guess that it would be easier for you to create a separate .NET object that is a wrapper around the functionality of GZipStream that you want to use. You can then expose your object to COM, and then VBA should make use of it.
Note that the assembly containing your COM object (and its type library too, I think, although I'm not positive on that) need to either be in the same directory as the main executable (winword.exe, or whatever) or in the GAC. This is due to the CLR's loading rules for assemblies.