It's difficult to answer for the 17th century as a whole. At the beginning of the 1600s, probably not. By the late 1600s, yes, courtesans in Edo had crests (mon). There were both brothel crests and personal crests of courtesans, and this adoption of crests was part of a larger trend, which really hit its stride in the 18th century, in which every Edo shop/restaurant/brothel/inn etc. adopted its own crest. There weren't any laws requiring or regulating these commercial crests. They were the products of the creators' imaginations, and served as trademarks for their business. Though most prevalent in Edo, the commercial use of crests spread across Japan, and of course continues today with corporations like Mitsubishi, whose familiar crest (a stylized version of Tosa's Yamauchi clan crest) we see on a regular basis.

There is a lot of evidence for the crests of courtesans and brothels in guide-books to Yoshiwara's courtesans, and generally, in ukiyoe prints The first Yoshiwara guide-book was the Yoshiwara Pillow Book (Yoshiwara makura) of 1660 which does apparently represent courtesans with the crests of their brothels, though I don't know if these advertisements actually reflected the real courtesan's costumes. Here's an image of a courtesan wearing her brothel's crest from another 1660 work, The Mirror of Yoshiwara (Yoshiwara kagami. (Image as reproduced inUt pictura amor: The Reflexive Imagery of Love in Artistic Theory and Practice, 1500-1700, p. 93)

There are also descriptions of top courtesans in a 1720 guide, each with crests. The following crests are listed pp. 96-98 in Cecilia Segawa Seigle's Yoshiwara: The Glittering World of the Japanese Courtesan.

Takao of the House of Miura Shirozaemon, Kyomachi. Supreme very best. Crest: maple leaf in a circle.

Usugumo at the same house. Supreme very best. Crest: ivy leaf without a circle

Otowa at the House of Yamaguchi Shichiroemon, Edocho. Supreme very best. Crest: double chrysanthemum shaded and white.

Hatsugiku at the same house. Supreme very best. Crest: same as Otowa.

Shiraito at the same house. Peerless very best. Crest: three cedar fans.

Miura at the House of Miura Jinzaemon, Kyomachi. Supreme very best. Crest: paulownia, or a four-eyed knot.

There are many references in 18th century texts and onward to courtesans wearing a personal crest. They become an essential part of the courtesan's brand. Segawa Seigle records how top courtesans would have their crests on their bedding, handkerchiefs, jackets, and other belongings and give gifts with the emblems to their attendants/musicians/support staff etc. If you haven't already read Segawa Seigle's Yoshiwara book, it's indispensable reading on the subject.

I've run into a problem, though, with trying to research courtesan/brothel crests. My searches show me that art books have a lot of examples/explanations of the crests, but art books are also the least likely to be electronically available, even in small previews on Google Books. I would really need to go to a physical library and peruse their ukiyo-e/shunga books, which I probably won't have time for. But if you're interested in learning more about the crests, the direction to take is through art history. Searching Google Books for keywords such as ukiyoe brothel crest will give you the tiniest tantalizing snippets of information, but enough to identify art books you could check out.