Yes you can drive through Red Rock Canyon and it's a breath taking view to drive through the loop through Red Rock Canyon.
The road that goes through Red Rock Canyon road offers a very pretty, relaxing and memorable drive or even a great bike ride with access to numerous trails and overlooks.
The Red Rock Canyon Scenic Drive is 12.5 miles long if you drive straight through and about 13 miles long if you pull off at each of the various overlooks.
I highly recommend taking a drive through Red Rock Canyon as it's a very good place to visit.
You'll likely want to come back and drive through the Red Rock Canyon a few more times or even more often.