If your pedal can operate with a single 9V battery, yes.
If the power jack on the pedal is labeled 9VDC and uses less than 1700mA (virtually all pedals use far less current than that), yes, the 1 SPOT can power it.
The 1 SPOT is 9VDC (not AC), with a barrel-style output plug which is center negative. The polarity symbol looks like this:
The Converter Plugs (CL6, C35, CYR, CBAT) allow the 1 SPOT to work with other types of DC power jacks and/or opposite polarity.
Most pedals use the barrel-style power jack with the polarity described above. For most others, one of the 1 SPOT Converter Plugs should make it work.
If your pedal requires 12VDC, 18VDC, 24VDC, or any voltage shown as AC, the 1 SPOT will not power it. (You can try a 1 SPOT with a 12VDC pedal, but it might sound a bit different. No damage will occur.)
The only exceptions are some Line 6 pedals (like the DL4, etc.) which show 9VAC on the pedal, but can actually be powered by a 1 SPOT with a CL6 Converter plug attached.
Occasionally, some pedals do not share power very well with other pedals, but this is rare.
In most cases, you can link your pedals with Multi-Plug 5 or Multi-Plug 8 daisy-chain cables, having all of them sharing a 1 SPOT.
If you have a fuzz pedal that uses germanium transistors, it probably cannot be used on a daisy-chain cable (MC5, etc.) with a 1 SPOT. It would need a separate 1 SPOT just for that pedal.