Depends when in the hand it happened.
You will often find they have a no flop no drop policy, which basically means if there isn't a flop then they don't take any rake.
As for after the flop I can't remember for sure, believe if you are playing no limit then the bet will count, though I have seen from when I have played limit that if someone doesn't call the bet and they just fold then your bet won't push it to the next boundry.
I am not 100% sure about that, its one of the things I don't pay too much attention to at the at the table.
In your example though as there was no flop, most sites won't rake it at all.