To receive an SVFR clearance, does the airport need to be reporting IFR conditions?
A Special VFR (SVFR) clearance may be issued to a pilot when:


The weather is below VFR weather minimums, as reported at the intended airport
The pilot is able to remain clear of clouds
The pilot has at least one mile flight visibility (other than helicopters) at all times
The pilot is operating (or wants to operate) within the lateral boundaries of the airport surface area
The pilot specifically requests it.  
The airport is not among those listed in 14 CFR Part 91, Appendix D (except helicopters)


If the weather is not reported at the airport, the pilot must tell ATC that they are "unable to maintain VFR" and request SVFR.

Side note:  The weather conditions that you describe above are technically "Marginal VFR" and not IFR.  It would be a perfect situation to operate SVFR though.