I'm not a big fan of covering this stuff over. Seller Disclosure is the first thing that comes to mind should your 'area' (or should future laws) require such disclosure when you sell. Also, the new siding mfgr. may have Warranty 'issues' with installing over the shingles. Breakage DOES occur since you have to either nail your sheathing over the shingles or screw your sheathing. With that, you 'compress' the rigid shingles.
In most jurisdictions (1 of which is mine), a homeowner can remove these shingles w/o the need to call in a professional Abatement Contractor. (Check the laws in your Municipality.) By following some common-sense guidelines, the removal is safe and easy. Disposal is another matter so check into this BEFORE you decide to do it yourself. (I had no problem w/finding a hauler ...)
As far as the moisture problem, you probably won't affect that, depending on what's under the existing sheathing.