No, you are defending your meaningless answer. As JesseM says:AT - you are being pedantic to defend your incorrect answer
it's pretty meaningless to talk about coordinate acceleration in general relativity without specifying a choice of coordinate system
Well you assumed two things arbitrarily:you are the one who arbitrarily assumed a specific category of acceleration.
1) specific category of acceleration : coordiante acceleration
2) specific frame of reference where the coordiante acceleration is not zero
Not in General Relativity. As DaleSpam already stated:the "general" definition of acceleration is exactly as i stated, and includes changes in direction.
And the original question was even specifically about the acceleration experienced by the object. This term usually refers to absolute proper quantities like proper time, which is the time experienced by the object.Traditionally the unspecified word "acceleration" is understood to refer to "proper acceleration" by default.