Ugh ... I'm afraid the answer is NO. It appears the tool still uses the "copper-to-drill" rule once unused pads are removed.
I even tried adding an anti-pad to the inner layer via pad stack definition with no effect.
I did have some success setting my copper-to-drill clearance to take into account my via pad, but I think this becomes one rule that is applied to ALL vias.
There are two options for setting this up, Used Design Rules or Use Pad Stacks. You should also check your Drill Oversize setting, especially if using design rules method w/remove unused pads set. You should be able to get the desired results either way but it may take a bit of effort.
That's the conclusion I came to. Thanks! I also submitted this as a "PADS Layout Idea" (Create option in via pad stack to identify it as "high-speed" or "remove unused pads" ) so Mentor can consider making this simpler.