Sure you can, but is it what you need to accomplish your goals? I do yoga but use it primarily for flexibility and stress relief. Flow yoga (vinyasa) may be challenging at first, but once your body adapts in about 6 weeks, there are minimal strength or cardio gains.
A more efficient use of your time to meet well-rounded fitness goals would be to add strength training 2 or 3 days a week (probably 2 at first). There's lots of good exercises here and you don't need a gym. Body weight exercises like squats, lunges, pushups, dips, etc. are a great place to start if you are new to strength training. During cardio, you burn calories while you are doing the activity. Muscle tissue is metabolically active, meaning the more muscle you have, the more calories you burn event at rest. It is a great way to stoke your metabolic furnace. Plus, as you lose weight, it helps offset the saggy skin look.