Will a change in the amino acid sequence of a polypeptide chain always change protein activity?

Not always it depends on where the aminoacid is located and how different it is from the normal one.
Proteins or polypeptides are molecules with a complex structure. There are four levels of structure from the aminoacid sequence to the attractions between the different aminoacids so you have to imagine it as a 3D structure.
Once you have that image think that there are parts of a protein that are active (which have enzyme activity for example) and others that are just structural. If an amino acid is exchanged for a similar one or is in a place that doesn’t have important chemical bonds it may have no effect on it’s activity.But if the change occurs in the active site or it changes it’s structure drastically it may have important implications on its function.
A very illustrative example is the haemoglobin and sickle cell anemia. Haemoglobin is the molecule that transports oxygen in red blood cells. In this illness one of the four haemoglobin chains (the chain) has a puntual aminoacid change: A glutamic acid is changed for a valine. This affects the structure which makes the haemoglobin polymerizate under low oxygen conditions.
This affects the red blood cell structure and makes it’s membrane more fragile which eventually breaks. This is what causes the haemolytic anemia.
So the answer isn’t yes or no. It depends on where it is and who it’s changing itself with.