No you can't not yet anyway:
That being said, however, my guess is that it will be a future addition or upgrade.
Maybe not with gearbox or other editors but perhaps an editor adapted specifically for the valve/spider series that allows backup and easier PC creation and storage and transferal of tones: (A huge request by many people so you can bet they're looking into it to sell more units since this seems to be a major deciding factor before some will take the plunge.)
Gearbox tones are not compatible with the SVMkII so you will not be able to upload tones to it through an FBV MkII.
You should certainly log a feature request for this though.
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