AN A300 CREW; ON A GAR AT KMEM; HEARD ONLY PART OF TH CLRNC; THEY MAINTAINED THE CLRNC ALTITUDE AND FOLLOWED THE PUBLISHED HDG INSTEAD OF RWY HDG AS INSTRUCTED.

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ON ARRIVAL INTO KMEM A MISSED APCH WAS REQUIRED TO RESOLVE AN ABNORMAL COCKPIT INDICATION. WHILE EXECUTING THE MISSED APCH MEM TWR INSTRUCTED US TO CLB TO 3000 FT MSL. APPARENTLY THEY ALSO INSTRUCTED US TO FLY RWY HDG; HOWEVER WE FLEW THE PUBLISHED MISSED APCH PROC WHICH DIVERGES FROM RWY HDG. NEITHER THE CAPT NOR I QUESTION THE RWY HDG CLRNC; BUT NEITHER OF US RECALL HEARING IT. WHAT WE BELIEVE HAPPENED WAS THAT THE RWY HDG CLRNC WAS ISSUED AND WE ACKNOWLEDGED IT. HOWEVER IN A VERY BUSY TWO PLT COCKPIT WHILE EXECUTING A MISSED APCH IN IMC WX WITH WINDSHEAR ADVISORIES AT THE ARPT AND AN ABNORMAL COCKPIT INDICATION TO DEAL WITH; WE FAILED TO ACTUALLY 'LISTEN' TO THE WHOLE CLRNC ('FLY RWY HDG; CLB TO 3000 FT'). TWR LATER ADVISED US OVER THE TELEPHONE THAT THERE HAD BEEN A POTENTIAL CONFLICT WITH ANOTHER ACFT. THEY WERE VERY CONGENIAL AND COOPERATIVE; BUT WANTED TO POINT OUT OUR DEV. THE CAPT; IN TURN; WAS CONGENIAL AND COOPERATIVE IN HIS TELEPHONE CONVERSATION WITH THE CTLR. I FEEL BADLY THAT WE MAY HAVE CONTRIBUTED TO A POTENTIALLY DANGEROUS SIT. AS A RESULT OF THIS OCCURRENCE MY VIGILANCE WILL BE AT AN EVEN MORE HEIGHTENED LEVEL WHEN FACED WITH TIME COMPRESSED; MULTI-TASKED SITS.