No! Even if you've worked with them in the past, it is not okay to send them messages unless they specifically asked you to do so.
Example ✔️
Buyer: Hey, please contact me when you are free to work on a new project
Seller: No problem, I'll let you know when my schedule is cleared up.
(Week later)
Seller: I finished the last project I was working on last week. I'm ready to get started when you are.
Example ❌
Seller: Hi, Happy New Year! Just wanted to say hi and let you know if you have any work I'm available.
(Buyer didn't ask to be contacted. This message is unsolicited. It only takes a few buyers marking this as spam for it to ruin your Fiverr account.)