Does it make a big difference in the flavor of my latte if I boil the milk, versus steaming it?
A latte is similar to a cappuccino but with different proportions. It's unsurprising that a similar method and equipment would be used. Cappuccino needs steamed milk to get the froth, so a coffee bar machine has a steam pipe. To boil the milk for a latte would require an extra piece of equipment and the associated space.
Is perfectly possible to make an espresso-based drink with milk heated on the stove or in a microwave, that would be a close approximation to a latte -- possibly indistinguishable. But if you boil the milk, it will change the flavour.
Steaming solves for the dual-purpose of both heating as well as creating the froth (milk foam). The froth is formed when the steam condenses onto the surface of the milk and these air bubbles are stabilized (do not collapse) thanks to whey molecules surrounding them.
You could also boil the milk but then you'd have to froth it separately.