Based on other users' threads, I would say "often but not always".

Also, it won't be all data, just the categories covered by Sync (you can review what you sync on the Options page, Sync panel).

If you need a more complete transfer, you may need to do it the old fashioned way with copies of files and folders. Hopefully it's not too late to make a backup of your Firefox data?

You can copy certain files with Firefox closed to the current profile folder to transfer or recover personal data.

• https://support.mozilla.org/en-US/kb/profiles-where-firefox-stores-user-data

Note that best is to avoid copying a full profile folder.

• bookmarks and history: places.sqlite
• favicons: favicons.sqlite
• bookmark backups: compressed .jsonlz4 JSON backups in the bookmarkbackups folder
• cookies.sqlite for the Cookies
• formhistory.sqlite for saved autocomplete Form Data
• logins.json (encrypted logins;32+) and key4.db (decryption key;58+) for Passwords saved in the Password Manager
  key3.db support ended in 73+; to use key3.db in 58-72, make sure to remove key4.db
• cert9.db (58+) for (intermediate) certificates stored in the Certificate Manager
• persdict.dat for words added to the spell checker dictionary
• permissions.sqlite for Permissions and possibly content-prefs.sqlite for other website specific data (Site Preferences)
• sessionstore.jsonlz4 for open tabs and pinned tabs (see also the sessionstore-backups folder)