It depends on the award. I’ve tried reading a couple of Orange Booker Prize finalists or winners and haven’t made it through the first chapter. I can only conclude that means those awards recognise a style of writing I’m not especially interested in reading.
As a child, I realised one of my favourite novels had won something called the Newbery Medal.
If I saw a Newbery Medal award on a book cover, I’d then read it because I found they were consistently enjoyable books.
As an adult, it depends …
As a book reviewer, I tend to mostly read pre-release or newly released titles. I”m always happy when I see a book I read and enjoyed finals or wins an award like the Carols (from American Christian Fiction Writers), the Christy Award (from ECPA), or the Inspys (organised by a group of book bloggers). I will occasionally buy a book that’s won one of these awards, especially if the publisher has a post-award sale 🙂
I would buy more Carol, Christy, and Inspy-Award winning books if it wasn’t for my current to-read pile. My current Kindle contains enough unread books to keep me quiet for the next two years, assuming I don’t download or agree to review any more books (as if). Then there’s my old Kindle Keyboard, which has enough books for the next eight to ten years …