Yes but only as far as the reflection spectrum of the FBG does at least partially overlap with the spectrum of the light source that is embedded into the OTDR. If they don't, you might see something only in case of poorly manufactured FBGs that reflect wavelengths outside their nominal spectrum.
OFTR (Optical Frequency Domain Reflectometer) might better suit your needs. Also I know Sentek Instrument used to manufacture an ODTR Spectrometer with a bandwidth of 4 nm, but I don't know whether it's still available or not.