Yes, but not as efficiently. The reaction between milk and the complex of enzymes in rennet is specific to each type of ruminant. Cheese made with cow milk requires rennet made from the stomach of young calves. Goats cheese require goat rennet, etc...
Rennet allows your milk to coagulate without the acidity levels getting too high -- in other words, it can make cheese from milk that is still sweet. For a soft cheese like chevre, queso, paneer -- lemon (or vinegar, or citric acid) can be all that you need to get the curds you want. But, for mozzarella, you need both a little initial acid ...
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