FLC OF A C337 SUPER SKYMASTER FAILED TO FOLLOW RWY HDG AFTER INITIAL CLB RESULTING IN ARTCC RADAR CTLR INTERVENTION IN CONFIRMING THEIR ACTUAL CLRNC BY THE DEP TWR CTLR.

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AN IFR DEP WAS MADE FROM PAH ON RWY 14. CONDITIONS AT THE FIELD WERE VMC. THE CREW CONSISTED OF THE CAPT AND COPLT. THE IFR CLRNC WAS CLRED AS FILED; CLB TO 3000 FT; CONTACT ZME 133.65 AND AN ASSIGNED XPONDER CODE. AFTER CONDUCTING ENG AND SYS CHKS; THE CAPT CALLED TWR FOR TKOF CLRNC. THE TWR CLRED THE ACFT TO TAXI INTO POS AND HOLD. PRIOR TO POS AND HOLD CLRNC BY TWR; GND CTL ADVISED AT THE END OF OUR IFR CLRNC THAT ZME REQUESTED A MINIMUM DELAY ON DEP. TKOF CLRNC FROM TWR WAS CLRED FOR TKOF; MAINTAIN RWY HDG. AFTER TKOF; TWR INSTRUCTED US TO CONTACT ZME AT APPROX 700 FT INDICATED. THE CAPT CONTACTED ZME; ZME CLRED US TO CLB TO 9000 FT. I BELIEVE THEY ALSO STATED RADAR CONTACT. AT THIS TIME A L TURN WAS STARTED. APPROX 30 SECONDS TO 1 MIN LATER; ZME ASKED US IF WE HAD BEEN ASSIGNED RWY HDG BY PAH TWR. THE CAPT RESPONDED THAT WAS CORRECT. AT THIS POINT; A RED FLAG WENT UP AND THE CAPT ASKED CTR IF THEY WANTED US TO TURN TO A SPECIFIC HDG. ZME ADVISED NEGATIVE; THAT WE WERE ALREADY CLR OF THE TFC. THE FLT CONTINUED TO DEST WITH NO FURTHER PROB. I FEEL THE CONTRIBUTING FACTORS TO THIS OCCURRENCE WERE: 1) FAILURE OF THE CAPT TO ENSURE THE PF WAS AWARE OF THE ASSIGNED RWY HDG CLRNC BY TWR. 2) A FEELING OF IMPORTANCE TO ASSIST WITH CTR REQUEST CONVEYED BY LCL CTLRS TO HAVE MINIMUM DELAY. 3) WX CONDITIONS (UNLIMITED CEILING AND 10+ MI VISIBILITY) THAT DOWNPLAYED THE IMPORTANCE OF IFR CLRNC INSTRUCTIONS. 4) FAILURE OF THE CREW TO HAVE CONTINUALLY POSITIVE COM BTWN BOTH CREW MEMBERS.