How we define Magic. If we mean spells like wizards do then not. It seems that only wizard and witches and other beings like elves or goblins can make spells or something like spells. Other magical beings like dragons and unicorns are not intelligent and have magical powers like flying, throwing fire and all of the things that a magical animal can do.
But Dementors are in a third category, they aren´t beings that are born but some kind of spirit like poltergeist and boggarts.
So in a sense they are magic. All of their characteristics are intrinsecal to them and are not a power of a spell like a magical animal but they are not really alive.
Think of Dementors like a autonomous spell, they do not produce spells but are a spell .
We know that a Wizard breed Dementors in Azkaban, they breed with depresion and other spirits like poltergeist are the results of spells so this define their characteristics, a pure magical being like a ghost but not being neither alive or death.