Yes, the standard chess position is one of the 960 different ways of arranging the back-rank and in fact is referred to as SP518 (start position number 518). Don't forget the rule about bishops having to be on opposite colours (which makes sense of course). A few of us 960 players have actually fluked the 1/960 chance of getting the standard position and it is fun when it happens, to reminisce about the old game.
The rules for setting up chess960 is that you need a rook on either side of the king. So can't you set up chess960 the EXACT SAME way as standard chess?