There is a chance you could.
If there are any leaks in the system, they could have been plugged up with the conventional oil sludge.
When you put synthetic in there, it'll break that stuff down and open up the leaks.
This of course only happens if there were leaks to begin with, so I wouldn't be too worried about it.
If you buy used, you should ask what kind of oil was in it when you bought it.
How could you tell it was conventional oil in the first place?