What you're describing is the reason many people work different muscle groups on different days. In short, yes, you can.
Let's say your aerobic activity worked your legs primarily, stationary bike for example. The next day may be a great day to do arms. However, you may want to gives your legs some rest.
Aerobic activity is building a different type of muscle than anaerobic activity, refer to: http://sportsmedicine.about.com/od/anatomyandphysiology/a/MuscleFiberType.htm
Let's keep in mind that you should be exercising every day, but that doesn't necessarily mean a grueling workout. If your primary concern is your heart (which it probably should be and is!), then make sure to never overlook cardio. Lifting weights, on the other hand, can help to boost your metabolism and offers benefits of its own: posture, strength, endurance, etc.