ACR B737 ACCEPTS QUESTIONABLE VFR CLB THAT PUTS THEM IN CONFLICT WITH ANOTHER B737 ENTERING DOWNWIND ON APCH.

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TKOF CLRNC WAS RECEIVED FROM TWR AT APPROX XA42. FLT WAS FROM SLC VIA THE MILFORD DEP; TO A SOUTHERN CALIFORNIA ARPT. TAKING OFF FROM RWY 34L AT SLC; TWR ISSUED INSTRUCTIONS FOR A HDG TO 260 DEGS AFTER DEP. OUR ALT LIMIT WAS THE ORIGINAL 11000 FT ON THE SID. COPLT WAS FLYING THE ACFT ON THIS LEG; THE THIRD OF 3 FOR THE DAY. ONCE ESTABLISHED ON THE 260 DEG HDG; I FINALLY WAS ABLE TO CONTACT SLC DEP CTL AROUND 8000 FT MSL. DEP CTL CLRED US TO CLB TO 12000 FT. BOTH OF US THOUGHT THAT STRANGE; SINCE THAT IS THE ALT ARRIVING ACFT ARE GIVEN FOR ENTERING THE DOWNWIND PATTERN. THE COPLT ASKED ME FOR A VFR CLB; SO I IN TURN REQUESTED ONE FROM DEP CTL. DEP CTL IMMEDIATELY RESPONDED WITH A TURN TO 180 DEGS AND A CLRNC TO 'CLB TO FL230; MAINTAIN VFR BELOW ONE-FIVE THOUSAND.' I REPEATED THE CLRNC; AND THE CTLR CAME BACK WITH AN AMENDED HDG OF 160 DEGS. THE ORIGINAL 180 DEG HDG WAS AIMING US DIRECTLY TOWARD A MOUNTAIN RANGE TO THE IMMEDIATE SW OF THE ARPT. THE 160 DEG HDG PUT US JUST OFF TO THE E OF THOSE MOUNTAIN PEAKS. ALTHOUGH WE HAD A FULL LOAD OF PAX; WE WERE FAIRLY LIGHT WT AT AROUND 110000 LBS TKOF GROSS WT. WITH A 250 KT SPD RESTR (UFN) FROM OUR ORIGINAL ATC CLRNC; WE WERE CLBING AT A RATE OF APPROX 4500 FPM. AT APPROX 11000 FT (COULD HAVE BEEN MORE OR LESS) DEP CTL ADVISED WE HAD TFC AT OUR 3 O'CLOCK POS AT 13000 FT. I LOOKED AROUND; PAST MY COPLT; AND IMMEDIATELY SAW A GLINT OF THE LOW SUN IN THE W SHINE OFF OF METAL. WE HAD RECEIVED NO TCASII WARNING OF ANOTHER ACFT IN THAT POS. I IMMEDIATELY ANSWERED 'GOT HIM!' AND LOOKED AT OUR ALT. IT WAS 11500 FT AND CLBING RAPIDLY. I LOOKED BACK AT THE OTHER ACFT AND COULD IMMEDIATELY TELL IT WAS ANOTHER B737-300 (SHAPE OF COWLS). THE TCASII SHOWED AN IMMEDIATE RA CONFLICT; WITH RED ON THE ENTIRE DIAL! IT WAS TOO LATE TO LEVEL OFF AT 12000 FT WITH OUR HIGH CLB RATE (PUSHING THE NOSE OVER WOULD ALSO HAVE SENT US SCREAMING TOWARD THE MOUNTAINS!); SO WE CONTINUED THE CLB TO GET OUT OF THE OTHER ACFT'S WAY. I ESTIMATE THE HORIZ CLRNC AT 8 MI WHEN WE CLBED THROUGH 13000 FT. A COUPLE OF FACTORS WERE PRESENT HERE: 1) WHEN ATC CLRED US TO 12000 FT (WHICH IS NON STANDARD -- EITHER WE MAINTAIN OUR ORIGINALLY CLRED ALT OF 11000 FT IF THERE IS INBOUND TFC; OR WE ARE CLRED TO FL230 IF THERE IS NOT TFC). I SHOULD HAVE REALIZED THERE MIGHT BE TFC IN THE AREA AND NOT HAVE ASKED FOR A VFR CLB. 2) WITH ATC AWARE OF A POTENTIAL AIRSPACE CONFLICT OVER THE MOUNTAINS; HE SHOULD NOT HAVE ISSUED US CLRNC FOR A VFR CLB. THE SIMPLE STATEMENT; 'UNABLE' WOULD HAVE SOLVED THE PROB BEFORE IT BECAME ONE.