Yes, the Grimm brothers tale is based on earlier works and folklore. As a rule, the Grimm brothers fairy tales were all existing folk tales.
The Sleeping Beauty (which I'm focusing on instead of Snow White, since it contains the same key element, and it's easier) story derives directly from Charles Perrault's "Sleeping Beauty" (La Belle au bois dormant), and published in his collection "Histoires ou contes du temps passé". The first half of it is very much the familiar (ie. Disney ± 1 dragon) narrative.
The older stories it draws from mostly somewhat miss the true love's kiss detail, unfortunately. Instead, a splinter holds the woman asleep, a our noble hero fails to wake her, proceeds to have sex with her, and nine month later she (still asleep) gives birth, and her newborn sucks the splinter from her finger, causing her to awaken. A well known version of this is "Sun, Moon, and Talia" by Giambattista Basile, and perhaps the earliest is “Histoire de Troïlus et de Zellandine" from "Perceforest" (which I couldn't find a good source of online).
There some possibility that sleeping beauty could draw some inspiration from the story of Brynhildr in the Völsunga saga (Chapter 20), who Odin punishes by putting to sleep with a sleep-thorn, until she is saved by one who does not "know the name of fear" (Sigurðr, who she later marries):
Odin, in vengeance for that deed, stuck the sleep-thorn into me, and said that I should never again have the victory, but should be given away in marriage; but there against I vowed a vow, that never would I wed one who knew the name of fear.
The Story of the Volsungs, trans. William Morris and Eirikr Magnusson, Chapter XX