CE650 FLT CREW REPORTS TCAS RA WITH UNKNOWN ACFT JUST BELOW AN OVERCAST LAYER AT 2800 FEET.

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WE WERE DSNDING VIA IFR CLRNC TO THE TERMINAL AREA FOR CWS. 5 MI S AND LEVEL AT 2800 FT; WE EXPERIENCED A TCAS ALERT FOR TFC; FOLLOWED SOON AFTER WITH A WARNING TO NOT DSND; AND THEN CLB. THE TCAS INFO SHOWED TFC POP UP AT 400 FT AT OUR 12 O'CLOCK POS AND LESS THAN 1 MI AWAY. AT THE SAME MOMENT; ATC ISSUED A WARNING OF THE SAME TFC AND THE CTLR STATED THAT HE WAS NOT IN CONTACT WITH THIS TFC. WE CLBED FOLLOWING THE TCAS 200 FT AND CLRED THE TFC. ABOUT 1-2 MINS LATER; WE HEARD AN ACFT CALL ATC FOR AN IFR CLRNC. BASED UPON MY OBSERVATION OF THE WX DURING THIS CONFLICT; OUR TFC WAS EITHER IN THE CLOUDS WITHOUT A CLRNC; OR WAS LESS THAN 200 FT BELOW THE BASES OF THE CLOUDS. THE WX CONDITIONS AT THE TIME OF THIS CONFLICT WERE OVCST AT 2800 FT TO 2400 FT WITH BASES SCATTERED TO BROKEN AND RAGGED. WE COULD NOT HAVE DONE ANYTHING DIFFERENT; AND OUR EQUIP WORKED AS DESIGNED. OUR TFC COULD HAVE GOTTEN AN IFR CLRNC ON THE GND BEFORE DEPARTING; OR COULD HAVE REMAINED THE MINIMUM DISTANCE AWAY FROM THE CLOUD BASES. MY OBSERVATION IS THAT OUR TFC WAS OPERATED IN A VERY DANGEROUS MANNER; AND BY A CARELESS AND RECKLESS PLT.