The conversations policy is here:
https://www.etsy.com/help/article/4531?ref=help_search_resultThis would fall under "unsolicited advertising or promotions":
"Please also be respectful of other Etsy members, and do not use Conversations for the following activities:
- sending unsolicited advertising or promotions, requests for donations, or "spam"
If recipients mark your conversations as spam, your shop can be affected (suspended). Not worth it!