No, in general it will not. The acceleration and mass tell you only the total (net) force being exerted on object A at that moment. That is equivalent to the total force object A is exerting on all other objects (B, C, etc.) it is interacting with at that moment. However, the mass and acceleration do not tell you anything about the individual forces that object A exerts on, say, just object B.
If you are able to determine that object A is only subject to one force, then you can find that one force because you know it's equal to the total force. But that's the only case in which the mass and acceleration tell you about a specific force.