Using the elliptical will make your body lose weight more than it will gain muscle. Ellipticals largely target the lower body, and while you may see a trace of muscle gain, your calves will likely become shapelier more than bigger. Cardio of all forms does not provide enough load for your muscle to experience noticeable hypertrophy.
Elliptical machines come in a variety of shapes and sizes, all with varying functions. Most machines allow you to change the ramp and resistance, making it easier to target parts of your leg over others. Depending on the height of the ramp, the level of resistance and speed that you're moving, you can work your calves the entire time you are on the machine. While they will be working with every motion, it is possible to change the settings to make them work harder.
Cardio for Fat Loss
Cardio is typically done as a way to burn calories and fat. Harvard Health Publications shows a 155-pound individual burning approximately 335 calories in 30 minutes on the elliptical. Cardio is going to be better at burning the fat that surrounds your muscles. If you burn fat from around your muscles, they will become more prominent and may appear leaner.
Strength and Muscle Mass
Building muscle requires a certain degree of stress to be placed on your muscles. Muscle growth occurs after tiny tears are produced through strength training. The repair process is when the muscle fibers actually increase in size. The elliptical will not put enough load on your calves to produce these tears and make the muscle bigger. It is possible, however, to make your calves stronger. Muscle movement, especially with your body weight, can increase the strength of your muscles without increasing their size.
To make your calves bigger, you will need to do things like heel raises several times per week. Exercises that focus on that muscle will allow it to tone and increase in size. While cardio will be good at burning the layer of fat that covers your muscles, it will not be enough to change the size. Strength train two or three times per week to see a noticeable difference in the size of your calves.