I wonder if having a master password will make my login data saved in Firefox more secure given the fact that I use full disk encryption. The password database won't be exposed in plain text physically on the hard drive when it is locked anyway. Still I guess a master password may protect the login data from other processes running on the same machine. I have Firefox Sync enabled, if it makes any difference (if I understand correctly, it don't).
First things first, on most desktop OSes, any process running under your user account can intercept input targeted at any other process running on the same desktop (as opposed to running on someone else's desktop over RDP, or the "secure desktop" on which the Windows UAC prompts are displayed), so this won't protect against malware, as it can wait for you to come back and log your keystrokes, or display a pixel-perfect copy of the Firefox password prompt at the right time and wait for you to type your password.
But, a second master password may still be useful depending on your threat model.
Let's say you leave your (full disk encrypted) laptop unlocked and unattended and the janitor takes a look. Firefox is closed and the janitor gets the master password prompt upon opening it - the janitor can't login to your webmail and steal your secrets. Full of disappointment, he leaves. We assume here that the attacker isn't advanced enough to leave malware on your machine to capture the password upon your return.
Now, let's replay the above scenario but with a government-sponsored attacker instead of the janitor. They tamper with the machine and leave a piece of malware on it to capture your secrets when you type in the master password. However, you noticed the machine was tampered with and decide to no longer trust it so you never type in your password and destroy the machine instead.
The government agency is disappointed, fires the hackers and replaces them with a 5$ wrench (defending against that is out of scope for this particular answer).
Yes, enabling Firefox master password will provide additional security to your logins. You've also partially answered your question. Even though you've enabled full disk encryption, the master password will protect your logins from other processes.
For example, a malware which has been able to execute on your computer will be able to read the disk contents (like other local processes), but wont be able to read your Firefox saved logins due to the master password.