Post your question only once.
Depending on how you want it to work, it most likely can be done.
The questions arise with what exactly you want it to count:
If you want to tell how many times the button was clicked since the document was opened, then you can increment a variable (add 1 to it) each time the button is pressed. The variable will start at 0 each time the document opens.
If you want to tell how many times the button was clicked over the life of the document, then you need to save that variable to a field in the document each time the document closes. This is a bit more work, and may cause problems if it is automatically saving when the end user isn't expecting it.
If you want to tell how many times the button was clicked by multiple people using multiple copies of your document, then you would need to save and retrieve the click count from a server. This can be quite a bit more work.
Or track it in an accessable database or 'subscribed global' variable.
Since I'm not a programmer, what would the code look like for such an event? Thanks.