I don't believe so.
An investigation will be conducted regarding all
statements required in the application. This includes
taking the fingerprints and physical descriptive data of the
applicant. One copy of the fingerprints will be forwarded
to the FBI for a search of the applicant’s criminal records.
That said, the FBI is actually fairly efficient and not the real barrier to the process. What could realistically happen is not unlike surrounding counties where the application and printing are done on day 1, fingerprints are sent to FBI (or IAFIS used) and NICS check run. This should take a week or two even with load.
The reference check is really a joke. Not unlike a job application, anyone knows enough to just stack the deck with people that will just spew the required answers.
That said, the above IAFIS and NICS check are done and they file should be in front of the judge in two weeks. There is no reason that the individual should not have their permit in 30->45 days. If there were any 'red flags' then they could pursue secondary investigations such as interviews/reference checks as a substantiation for their decision.
State law cannot be trumped by the county...they have latitude to 'add on' not override. It is not a matter of county law but rather county overhead and bureaucracy in executing state law.
As far as the addendums added to CCW permits in Erie County...that is a political issue and not a legal issue in the hands of the judges. Unless the state were to pass a law repealing the right of the issuing officer to place restrictions, we are stuck. That said, if the state were to do so, I'm sure even more permits would find themselves indefinitely stalled out in the system. A catch-22 as it were.