Nick,
In the former case, you may, starting with live Type and the background object at the bottom in the stacinkg order:
1) Type>Create Outlines and Ungroup;
2) With everything still selected,Object>Path>Offest Path by the desired gap width, and Group, then lock, then Group the original outlined letters, then unlock;
3) Select the Offset Path Group and
3a) Also select the background object and in the Transparency palette flyout click Make Opacity Mask with both Clip and Invert Mask unticked, this is fully reversible;
3b) Also select the background object and Pathfinder>Minus front, this is irreversible and creates a Compound Path background object;
3c) Just change the a white fill, or whichever colour you have behind the background object if any.
In the latter case, you may start by Object>Path>Outline Path and then proceed more or less as in the former case as needed.