Based upon individual CHC books and the lesson plans, yes, CHC does fit the classical mold to a degree. The classical approach is a method of using materials or programs, and CHC does not box home schoolers in to a particular method. Catholicism itself is quite a classic so the fundamental basis of the CHC materials is toward classicism.
For clarity, let me explain further. A classical education begins by filling the mind with truth by listening, reading, seeing, touching and experiencing. Simply by taking a child to a traditional Catholic Mass will provide the child with a wealth of concrete truth. There are prayers and hymns to memorize, music to listen and sing to, statues to appreciate and sometimes touch, icons to focus one's attention, candles to light, and incense. And of course, the history behind it all is quite impressive spiritually, artistically, and intellectually.
The actual CHC first grade lesson plans provide guidelines for phonics, reading aloud, memory gems, math, science, social studies, religion, handwriting, art, music, and recess. This schedule provides time and guidelines for both book learning and hands-on learning. Wednesdays are flex time for adding an extra subject or for field trips. There is no commitment to follow the plans exactly as outlined. Because the books are sold separately from the plans, you have the option of substituting a different book for any subject. For example, if you prefer that your children learn italic handwriting, then you would substitute an italic handwriting workbook. If you are interested in adding Latin into the mix, you can fit Latin lessons in during music (the verb forms are chanted, after all) and social studies time or on Wednesdays.
Regardless of the approach you use, the subjects are important. You want to cover the core subjects thoroughly. In these areas, the CHC materials allow time for children to absorb facts and to practice using these facts, which is key to the classical approach. The CHC plans also distinguish between core areas and non-core subjects to allow you flexibility when your school day doesn't go exactly as planned. Because you mention that you will be starting to home school this fall for the first time, my recommendation is that you begin slowly. Get used to this new way of life by focusing on the core subjects during the first year of home schooling.
Happy home schooling,