Should Christians use other miracles to convert others?

[phat8594]

Might it not be possible that the man healed at the Bethesda pool didn't know the situation?

That is unlikely. The man is questioned himself by the Jews -- and even John says:

14 Afterward Jesus found him in the temple and said to him, “See, you are well! Sin no more, that nothing worse may happen to you.” 15 The man went away and told the Jews that it was Jesus who had healed him. 16 And this was why the Jews were persecuting Jesus, because he was doing these things on the Sabbath.

I think your statement would be more likely if the man didn't go to the Jews after already being questioned. But then again, that's my take on it.