As for whether AgSO4 exists or not, in the context of this question it doesn't.
I agree, but I believe we should refrain ourselves from stating things that are not correct when it is not necessary. So it is much better to say "product of this reaction is Ag
2SO
4" (which is unconditionally true) than to state "there is no AgSO
4 salt " (which is - in in general - wrong).
The difference between your answer (no such compound) and my answer (different product) is subtle, but very important.
Imagine that you are a chemist (I believe you are working in IT, not as a chemist, if not, I apologize in advance) and one of the persons you have trained at work remembered that you told there is no such thing as AgSO
4 - he will either hate you later as you have teached him wrong, or he will remember he had a retarted teacher, that even didn't know that Ag
2+ exists.
General idea is not to add unnecessary confusion when it is not needed. Teaching chemistry requires many simplifications at first, but it doesn't mean we have to give wrong information.
Just my philosophical approach to the teaching process.