Your alarm system will likely work "ok" with VOIPo (or other VoIP provider), in the narrow sense of properly getting alarm signals to the central station. However, unless your system has cellular backup, using VoIP may render your system much less secure.
First, you should connect your adapter to the line side of your RJ31X jack -- otherwise, the alarm won't work if the phone is in use, and an intruder could defeat it by simply picking up a phone.
Next, consider UPS protection for modem, router and ATA. Power often fails in a fire. Also, if your meter or main switch is mounted outside your home, an intruder could easily turn off power before entering.
Your alarm panel is in an obscure and possibly physically secure location. Be careful that your network gear can't be easily found and disabled before the alarm signal gets sent.
The combined reliability of your ISP, VoIP provider and equipment is probably much worse than your POTS line.
See »
connectedplanetonline.co ··· _030507/ ; also search for VoIP and RJ31X -- you'll find info on making a proper hookup.
Many folks consider their alarm system to be a joke. It's only there to get a discount on homeowners insurance, and they figure that the burglar will have driven off with the loot before dispatch arrives, anyway. If you depend on yours for real security, I strongly advise that you have a professional do (or at least review) your installation.