Yup. You should be burning roughly the same calories as you would had you done it all at the same time.
Increase your metabolism? You'll burn more calories for the day but it won't have much of an effect on your metabolic rate. If you want to increase/maintain your metabolic rate, you'll need to strength train and build muscle. Losing weight will decrease your metabolic rate, the less you weight... the less calories you burn. The more fit you become the harder you'll have to work to get the same calorie burn. When you lose weight (and are not strength training) you'll lose lean muscle along with fat. Muscle burns more calories than fat, so you're going to want to maintain that. Losing muscle will decrease your metabolic rate. Eating at a calorie deficit for a prolonged period of time decreases your metabolic rate.
So when you're losing weight you're decreasing your metabolic rate. Strength training is one of the main activities you can do to help prevent it to an extent.
At my starting weight I burned 1550 cals just existing. At my current weight I only burn 1300 cals- (BMR or basal metabolic rate).
But yes, walking is a form of cardio and as long as it gets your heart rate up... you'll be burning extra calories that day. Perhaps you are referring to it increasing TDEE (total daily energy expenditure)? If so, then yes. :) It will.