BECAUSE OF DISTR WITH TFC WATCH AND A POSSIBLE POTENTIAL CONFLICT; A DEP A319 FLT CREW FAILS TO FOLLOW THEIR FLT PLAN AND REVISED CLRNC ON DEP FROM CLT; NC.

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WE DEPARTED CLT RWY 18L ON RWY HDG. CAPT (PNF) NOTICED ACFT AHEAD OFF OF RWY 18R SEEMED TO BE SLIGHTLY CONVERGING. ATC GAVE US L HDG 165 DEGS JUST BEFORE WE ENTERED A LAYER OF CLOUDS. CAPT CONTINUED TO WATCH OTHER ACFT ON TCASII TO CONFIRM PATHS WERE DIVERGING. ATC GAVE US A 090 DEG HDG TO JOIN LILLS TRANSITION. ON ACTIVATION OF THE NAV MODE; OUR INTERCEPT POINT WAS JUST BARELY S OF SDZ ON SDZ 228 DEG RADIAL. WE ARE NOT CLR ON WHETHER WE WERE N OF THE CLT 112 DEG RADIAL TO LILLS AND; THEREFORE; WOULD NOT INTERCEPT THE RADIAL TO LILLS ON A 090 DEG HDG; OR IF CLT DROPPED OUT AS OUR FROM POINT AND WE FAILED TO INTERCEPT THE RADIAL FROM CLT TO LILLS. IN EITHER CASE; WE SHOULD HAVE CONFIRMED WITH ATC SINCE WE WERE BYPASSING LILLS. AFTER A FEW MINS; ATC ASKED US IF WE WERE PROCEEDING TO LILLS. CAPT REPLIED WE WERE ON A 090 DEG HDG TO JOIN; WHICH WAS DIRECT TO SDZ (CAPT MISTAKENLY CALLED SDZ; SANDUSKY; INSTEAD OF SANDHILLS). ATC SAID WE WERE SUPPOSED TO HAVE GONE OVER LILLS BUT HE WOULD ADVISE ZDC THAT WE WERE PROCEEDING TO SDZ AND GAVE US A FREQ CHANGE TO ZDC. ATC DID NOT INDICATE THERE WAS ANY TFC CONFLICT AND THERE WAS NONE INDICATED ON OUR TCASII. CAPT LET HIS PREOCCUPATION WITH THE OTHER ACFT DEGRADE HIS SITUATIONAL AWARENESS ON THE SID.