To receive an SVFR clearance, does the airport need to be reporting IFR conditions? If conditions at a towered airport are not IFR, can pilots request a special VFR clearance? For example, at a Class D airport, ceiling 1300 broken, 10 sm visibility is technically too low to remain in the pattern (assuming a 1000 foot AGL pattern and maintaining at least 500 feet below clouds), yet it is not IFR. 

With a Special VFR clearance, the pilot would be able to maintain a 1000 foot pattern and remain clear of clouds. If the pilot requests SVFR, will the tower grant it?
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.