Since the chains of immunoglobulins are held together by disulfide bonds, which are reduced by DTT, it is possible that DTT would interfere with the immunoprecipitation.
You can definitely give it a try. Dilute your IP lysates with IP buffer without DTT. In my experience upto 0.5 mM DTT have no effect on co-IP experiments.
It could through what Adam B Shapiro mentioned, but another thing to keep in mind is the DTT could affect the resin that's used. DTT is a no-go for TALON resins but ok for others, sepharose, FLAG, etc.