Answer
No
Work Step by Step
Since C, F and G are collinear, point C is a point on line $\overset\longleftrightarrow{GF}$. If $\overset\longleftrightarrow{AB}$ intersects plane M at point C, then $\overset\longleftrightarrow{AB}$ intersects $\overset\longleftrightarrow{GF}$ at point C.