For my very first batch, I didn't stir the solution. The result was that the bottles that were filled early were heavily over-carbed (I actually had 5 of them explode). The later bottles were barely carbed at all. It all depends on how much motion your racking process creates, I guess. Mine apparently didn't swirl the brew at all. After that first batch, I always stirred it and also added it little bits at a time through the entire racking process. Then, I started kegging and I don't have to worry about that any longer.
The bottom line is, you "might" be fine. My first batch had the sugar solution at the bottom, and I added the beer to it. Since you waited a bit before adding the sugar, it might be ok. But I would still be a bit careful for possible bottle bombs.