according to the Tor browser:

Fingerprinting is the process of collecting information about a device or service to make educated guesses about its identity or characteristics. Unique behavior or responses can be used to identify the device or service analyzed.

So, to answer your question, yes, fingerprint contribute to tracking. The only browser which really protect you from fingerprint is Tor browser since it aims to make all users look the same. The rest is just marketing and not real substance.

So, if you really need protection against fingerprint, use Tor browser.