Is there a particular reason for wanting to do this? Suitcase Fusion does it’s own ‘scan’ of fonts when you add them to the vault to help ensure that bad/corrupt fonts do not enter your workflow. There’s no real need therefore to do it again via Font Doctor on fonts that you’ve already added. Generally Font Doctor is used to check/fix fonts before you add them to Suitcase.
As you note, you can’t do a scan on the internals of the font vault, as Font Doctor can’t scan within the package file. Doing so would also risk something being changed that would stop Suitcase working and put it in an unsupported state. If you really need to scan all the fonts, you’d be best to extract copies of them from Suitcase. The simplest way to do that is to ‘select all’ the fonts and then ‘Collect fonts for output’.