SF340 ACFT HAD FAILED ENG ANTI-ICE; BUT CAPT ELECTED TO FLY THE NEXT LEG BECAUSE OF RPTED GOOD WX. ENRTE THE FLC ENCOUNTERED CLOUD LAYER AND BEING UNABLE TO FLY IN CLOUDS REQUESTED AND OBTAINED DSCNT CLRNC. RPTR FO QUESTIONS BEING ON AN IFR FLT PLAN WHEN THEY WERE UNABLE TO FLY IFR.

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ON THE PREVIOUS LEG WE LANDED IN PVD WHERE A PAX NOTICED SPARKS COMING FROM THE L ENG. CLOSER INSPECTION REVEALED THAT THE ENG ANTI-ICE PROTECTION HAD BURNED UP. SINCE THE WX WAS CURRENTLY VFR AT LGA AND FORECAST TO STAY THAT WAY; WE BOTH DECIDED THAT IT WOULD BE OK TO DO THE NEXT LEG WHERE MAINT COULD THEN WORK ON IT. THE CAPT TOLD ME THAT HE CALLED MAINT CTL ABOUT THE PROB. SINCE WE TOLD THEM ABOUT IT AND WROTE IT UP IN THE LOGBOOK; I THOUGHT ALL WAS WELL. THE PROB WAS THAT EVEN THOUGH IT WAS VFR; WE STILL ACCEPTED THE IFR CLRNC -- NOT ANTICIPATING ANY CLOUDS WOULD BE ON OUR RTE. WE WERE CLRED FROM 8000 FT TO 6000 FT ENRTE WHERE WE ENCOUNTERED A SCATTERED LAYER. I ASKED ATC IF WE COULD GET LOWER ASAP. ATC SAID THAT IT WOULD BE SOON. MY CAPT THEN TOLD ME TO EXPLAIN THAT WE NEEDED LOWER BECAUSE WE COULD NOT GO INTO ANY CLOUDS. I SAID THAT IF WE TELL ATC WE CAN'T GO INTO CLOUDS ON AN IFR FLT PLAN THEN WE SHOULD DECLARE AN EMER. HE SAID THAT SINCE WE WROTE UP THE PROB IN THE LOGBOOK THAT IT WOULD BE ALRIGHT. SO; I TOLD ATC THE PROB AND WITHIN A FEW MI WE WERE CLRED TO 4000 FT AND IN THE CLR. LOOKING BACK ON IT; WE SHOULD HAVE GONE VFR SINCE WE HAD NO ICE PROTECTION. IT WAS ONLY A SCATTERED DECK AT 6000 FT BUT THE CAPT WAS AFRAID WE MIGHT ENTER A CLOUD WHICH MIGHT FLAME OUT THE L ENG. BEING ON AN IFR FLT WAS A MISTAKE BECAUSE THAT IMPLIES THAT WE CAN PENETRATE THE CLOUDS IF WE HAVE TO; WHICH WE COULD NOT. I FELT COMFORTABLE WITH MAKING THE FLT UNDER THE WX CONDITIONS; HOWEVER; I SHOULD HAVE SUGGESTED WE GO VFR. ANOTHER CONTRIBUTING FACTOR WAS THE RELATIONSHIP BTWN THE CAPT AND MYSELF. THE CAPT IS NOT AN EASY PERSON TO GET ALONG WITH; BEING THAT HE HAS AN EXCESSIVE PERSONALITY AND IS A BIT OF A KNOW-IT-ALL. HE IS OVERBEARING AND RARELY ASKS FOR MY OPINION ON THINGS. I DON'T ALWAYS FEEL LIKE THE LINES OF COM ARE OPEN; SO WE DON'T ALWAYS DISCUSS THINGS AS MUCH AS WE SHOULD. THIS WAS ONE OF THOSE OCCASIONS WHERE MORE DISCUSSION PROBABLY WOULD HAVE PREVENTED MORE PROBS.