I would guess that I have using the following logic.
If one were to hit a ball every second, they would hit the millionth ball on day 11. Now lets break that down a bit. I would guess that the average person hits about 2 balls per minute when playing an opponent and about 4 when practicing by themselves. At a rate of 3 balls per minute, a person would hit their millionth ball on day 231. The previous numbers don't calculate for anything other than playing pool 24/7. Now break it down into actual playing time. It wouldn't be far fetched for someone addicted to playing pool to play for 4 hours in a day. At a rate of playing 4 hours a day hitting 3 balls a minute, one would hit their millionth ball after 3 years, 9 months, 2 weeks, and 4 days.
So while I'm sure that I haven't played 4 hours every day over a 3 period, I have played longer and shorter than 4 hours on many days over the course of 23 years. Therefore, I would be willing to guess that I've hit over a million balls.