Probably not. As a general rule we do not buy textbooks for the library’s collection, though some professors put their textbooks on course reserve, and you can ask your professors to do so.
You can use the Library Search on the library homepage to check if your textbooks happen to be in the library's collection. You may request these books from other UW campuses using Library Search, but you may not request textbooks through Interlibrary Loan. (Any book available through the campus bookstore is considered a textbook.)
The campus bookstore's website lists what textbooks are required for every class.