You can still get to Scotty's Castle. The road that's closed is the road that runs from Scotty's Junction on US-95 east of the park via NV-267 and Grapevine Canyon Road to the Castle. The road from the main part of the park to the south (the way you'd be coming), i.e. Scotty's Castle Road and Grapevine Canyon Road, is open but subject to delays of up to half an hour for construction. Yeah, that would make me think about skipping the Castle, with a total delay of up to an hour, and that's a shame. Still, there is plenty else to see in the park. You might ask at a visitor center if they know when traffic will be allowed through, if there's a schedule, or if it's just random.
AZBuck