AN ACR MLG CLBED IN RESPONSE TO A TCASII COMMAND AT NIGHT IN IMC.

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ON APCH AT CLE RWY 5R ILS 10 NM 'CLRED TO 3000 FT UNTIL INTERCEPTING GS; CLRED FOR APCH.' APCH ADVISED US OF TFC R TO L BELOW US AT 2500 FT. WE WERE IN IMC. THE TCASII PICKED UP OUR TFC AT OUR 3 O'CLOCK POS. I FIRST RECALLED IT AS BEING A RED CIRCLE AT MINUS 400 FT AND A TFC ANNOUNCEMENT; THEN IT CONTINUED TO CLB MINUS 300 FT AND (I THINK) MINUS 200 FT. AT THAT TIME WE RECEIVED A CLB COMMAND IN EXCESS OF 1000 FPM WHICH WE COMPLIED WITH. AT 3600 FT WE RECEIVED A 'CLR OF CONFLICT.' WE COMPLETED OUR CLB AT 3800 FT AND ADVISED ATC (CLE APCH) WHO ACKNOWLEDGED US AND REAFFIRMED THAT WE WERE STILL CLRED FOR THE APCH. WE COMPLETED A NORMAL APCH AND LNDG. WE DID CALL APCH AFTER LNDG AND THEY ADVISED US THAT THE TFC WAS ON A VFR FLT PLAN AND THAT THEIR EQUIP INDICATED AT LEAST A 300 FT SEPARATION WITH NO COLLISION ALERT. SUPPLEMENTAL INFO FROM ACN 236044: TFC HAD A PERPENDICULAR FLT PATH AND APPEARED TO CLB TO 300 FT BELOW OUR LEVEL. COULD NOT CONTACT ATC AS FREQ WAS VERY CONGESTED. (I OBSERVED VERT SEPARATION AT 200 FT DURING THE RA AS CLB WAS INITIATED.) ATC WAS CONTACTED BY THE CAPT AFTER LNDG. WE WERE ADVISED THAT THE TFC WAS ON A VFR FLT PLAN AND THAT RADAR INDICATED AT LEAST 300 FT SEPARATION AND NO COLLISION ALERT ON HIS EQUIP.