W/R/T/ preflop, there is no standard rule here. Most places allow (require) the BB to take his raise back and post his BB. In some of those places, he will not be allowed the option to raise if there is no raise in front of him - in others, he will.
Some places require that any chips that are placed over the line are comitted to the pot. This is a stupid rule for out of turn bets IMO. I got burned on this rule once. Now, if I am playing at that casino, if I am in seat 1 I will never act until prompted since I can't see seat 10.
As ruled, then BB should not have the option of raising. It would be akin to a straddle from the BB, raising the stakes for that particular hand after the BB looked at his cards. The obvious opportunity for an angle shoot here answers the question. No. Way. In. Hell. I mean, holy shit, I get to look at my cards, raise the stakes of the hand if I choose, and have the option to 3-bet myself????? No way. Whoever suggested otherwise deserves a KITN.