Yes, I would, assuming you don't mean statements like "1+1 = 2", but rather true statements spread over a variety of contexts such that I would reasonably believe that you would be trustworthy to that degree over random situations (and thus including such as whether I should give you money.)

According to game theory, this opens you to exploitation by an agent that wants your money for its own gain and can generate 100 billion true statements at a little cost.