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I think that depends on how new/old your FIOS box is - I've disconnected by battery but it still beeps. I've read online that newer ones stop beeping. Older ones like miine keep going (and going, and going... ahhhhh)
I agree with DanielL18 - A few years back I paid the replacement battery (although I didn't want it, and didn't care for landline during an outage). That battery has recently started beeping - but removing the battery doesn't stop the beeping, and holding the reset button only stops it for a short period of time before it starts again. I've just arranged for a tech to come out, which the agent assures me won't cost me. My understanding is that newer boxes will stop beeping after battery is removed - but older boxes like mine won't stop - ever - ever!!!
Raspberry Pi Class
Jedi Force Gestures Based Home Automation (with Smartwatch)
How to: Power (with Intel Edison)