RWY INCURSION BY LIGHT TWIN CREATES A POTENTIAL CONFLICT NMAC WITH DEPARTING TFC.

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DEPARTING HAYDEN; CO; SCHEDULED 121 FLT. MADE ALL POS RPTS ON CTAF 123.0 (PUSHBACK; TAXI; DEPARTING). ADVANCED THRUST; STARTED TKOF ROLL AND ACCELERATED QUICKLY DUE TO RELATIVELY LIGHT GROSS WT. SUDDENLY; A GA TWIN ENG ACFT PULLED OUT ONTO THE RWY. I COULD HEAR UNICOM BROADCAST TO THE GA ACFT THAT WE HAD JUST ANNOUNCED OUR DEP. WE HAD NOT YET REACHED DECISION SPD; I ASKED THE CAPT WHAT HE WANTED TO DO; THINKING TO MYSELF THAT; IF WE ABORTED AT THIS POINT; WE WOULD LIKELY FACE 1 OF 2 SCENARIOS: COLLISION OR DEP FROM THE RWY. I FELT WE HAD ENOUGH ROOM TO SAFELY ACCELERATE AND BECOME AIRBORNE OVER THE TFC. CAPT AGREED WITH MY THOUGHTS AND SAID; 'KEEP GOING.' WE LIFTED OFF SAFELY. THE ACFT HAD ALREADY QUICKLY EXITED THE RWY BY THIS TIME. NO FURTHER EVASIVE ACTION WAS NEEDED OR TAKEN. DUE TO RWY SLOPE; IT WAS NOT POSSIBLE TO SEE ACFT ON RAMP OR MIDFIELD TXWY FROM TKOF POINT ON RWY. I THINK THE PROBABLE CAUSE OF THIS INCIDENT WAS FAILURE OF GA ACFT TO MONITOR THE CTAF AND TO ANNOUNCE HIS INTENTIONS/MOVEMENTS; AND BE AWARE OF OURS. IT WOULD HAVE BEEN HELPFUL IF UNICOM (CTAF) COULD HAVE SEEN THIS POSSIBLE CONFLICT AND ALERTED US.