If you are that coordinated, yes! Keep a steady eye. Falling sucks.
Can my dog accompany me on The Oro Valley/Tucson Loop?
Yes. Pets are permitted. But you must keep your pet close to you. There are accidents between pets and cyclists and dog owners bear responsibility.
And please be sure to properly clean up and dispose of any waste. Also note that pets must be leashed (less than 6 feet) and may not cross the center line, staying to the right at all times.