The answer is YES, you can use directv standard equipment with directv HD reception equipment, the opposite is true but the HD reception equipment on a SD Dish will be restricted to SD input. The only caveat to that is SWM vs the older style connections, and the age of the reception equipment if the SD receiver in question will support the connection type of the dish.
in a simpler answer, if your standard box is new enough, it'll handle the newer dish, same with an older dish.
if it's an older box, it'll normally only handle the older dish , but in either instance there is backwards copatibility of HD dish to standard equipment.