The answer to this question depends on the person. It depends on the maturity of the person's perception of art, and of gardening.
If you ask someone who thinks that gardening is solely about growing potatoes, then the answer is definitely 'no'.
But if you were able to ask Monty Don, Simon Schama, or Carl Jung, you'd get a very different answer. And each of those people would probably have different reasons for saying that gardening is art.
I heard a quote on the Monty Don 80 gardens around the world that said, a garden is the only art-form we live in.....
Monty's 80 Garden TV series and book is packed with asides, and tantalising hints, about this question, as is his TV series and book about Italian Gardens. Monty also made a TV series, several years ago, about the symbolism of plants. Though that was about the use of plant forms IN pictorial art, rather than the act of interacting with nature.
The answer depends on the individual. It's very curious that all of the people who have decided post replies on this thread might be classied as a 'certain type' of gardener. I suspect that many other gardeners will notice the title of this thread, and dismiss it. People react in different ways, both to the question, and to their own gardens.