The short answer is, "Yes, but they're not real excited about doing so". Plus:
...[I]t would be unwise to assume that the fire department is going to use advanced cat-rescue techniques.
Firefighters in Okinawa, Japan, earlier this year decided the best way to deal with a feline up a 60-foot tree was to grab a chain saw and lop off the section the cat was clinging to.
When a Tennessee woman's cat was stuck in a pine tree, firefighters gave her two options: they could blast it out with a hose or shake the tree until the cat fell out. When asked how option B was any different from the cat's just falling out on its own, one firefighter answered, "Neither is real different, ma'am. Just quicker."