TCASII ALERT AND FLC FOLLOWED RESOLUTION COMMAND; DEVIATED FROM ASSIGNED ALT; THEN RETURNED.

Narrative

BNA TRACON WAS PROVIDING RADAR VECTORS TO THE ILS RWY 20R APCH. ATC CLRED OUR FLT FOR THE ILS APCH APPROX 12 MI NE OF BNA AT AN ALT OF 4000 FT MSL. ABOUT 10 SECONDS LATER; ATC CANCELED OUR APCH CLRNC AND DIRECTED US TO TURN R TO A HDG OF 270 DEGS. WE NOTED ON OUR TCASII TFC AT OUR 12 O'CLOCK POS LESS THAN 2 MI AT 3000 FT AND CONCLUDED THAT WAS THE REASON FOR OUR CANCELED APCH. SHORTLY AFTER TURNING TO A 270 DEG HDG; ATC DIRECTED US TO TURN TO A HDG OF 360 DEGS. WHILE ESTABLISHED ON A 360 DEG HDG AT AN ALT OF 4000 FT; OUR TCASII ALERTED US TO TFC AT OUR 12 O'CLOCK POS ALT OF 3800 FT AND LESS THAN A MI. WE RESPONDED TO THE TCASII RA BY CLBING TO 4500 FT. FREQ CONGESTION PREVENTED US OF INFORMING ATC OF OUR CLB BY 10 SECONDS. ATC THEN DIRECTED US TO TURN TO A HDG OF 110 DEGS. AFTER TURNING; THE TCASII ADVISED US THAT WE WERE CLR OF THE THREATENING TFC AND WE RETURNED TO OUR ASSIGNED ALT OF 4000 FT. THE CTLR'S SEQUENCING PLANS FALLING THROUGH TOOK OUR ACFT OUT OF THE NORMAL FLOW. MODERATE TO HVY WORKLOAD FOR THE CTLR DIVERTED HIS ATTN AWAY FROM OUR FLT. NO TA WAS PROVIDED BY ATC; AND DUE TO THE FACT THAT WE WERE IN IMC; WE HAD TO COMPLETELY RELY ON THE TCASII TO AVOID A MID AIR COLLISION.