Fitbit requires Transport Layer Security protocol - TLSv1.2 for the subscriber endpoints. TLS+SNI is not supported. Self-signed certificates and all versions of SSL are also not supported.
Espruino is a JavaScript interpreter for low-power Microcontrollers. This site is both a support community for Espruino and a place to share what you are working on.
From fitbit docs:
From Espruino docs:
Which makes it seem to me like it could very well work. Don't know if the requirements listed on fitbit are too narrow or not.
I suspect you will have a better answer from someone else soon.