If I buy shares of a product that currently does not pay dividends, can it theoretically/technically start paying dividends in the future?
Yes, absolutely. Consider Microsoft,
Updated Jan. 17, 2003 11:59 p.m. ET
Software giant Microsoft Corp., finally bowing to mounting pressure to return some of its huge cash hoard to investors, said it will begin paying a regular annual dividend to shareholders.
From Wall Street Journal. Thus, for the years prior to 2003, the company didn't pay dividends but changed that.
There can also be some special one-time dividends as Microsoft did the following year according to the Wall Street Journal:
The $32 billion one-time dividend payment, which comes to $3 for each share of Microsoft stock, could be a measurable stimulus to the U.S. economy -- and is expected to arrive just in time for holiday shopping.
Course companies can also reduce to stop dividends as well.