There are no guarantees.
A modem use various protocols that form standards by which communications can be had between two similar devices over a standard POTS line. As the line conditions change, the modems can oftentimes re-adjust to accommodate.
An ATA attempts to emulate a POTS/PSTN line, but the analog stream from the modem is converted into data packets which are encoded using a voice codec. As your profile shows to be NA, you should use a G711u codec as this offers a wider frequency bandwidth. As the modem is using audio frequency tones (much like a fax) to communicate, the need is to use a codec that will support frequency bandwidth requirements such that tones are not compromised as they go from point A to B.
Now comes the tricky part.
The issues that arise are usually associated to the Internet carriage or local congestion and such. When traversing the network there are various issues that might arise that impair the delivery of the packets such that what was sent is not quite the same as what was received. Data packets from the sending modem may have looked like - 1, 2, 3, 4, 5, 6, 7, etc., but at the receiving end may look like - 1…2, 4,3, 5…6, 7. They may not arrive at the same timing interval nor may they always arrive in the same order and in some cases, some packets may not arrive at all. Most of the time, this is not an issue as carriers and ISPs have gone to great lengths to improve the networks as they recognize the growing significance of VoIP and similar technologies. The use of jitter buffers in the ATA may help on the receive end of things, but you still have to insure that when sending there is enough bandwidth available for all devices on the network such that the upstream is sent without issue. You may very well need to employ QoS on your router and ATA (I would anyway).
If it were me, I would base the decision on moving to VoIP on how mission critical is the device being monitored and the impact that it may cause if it does not work when most needed. The Internet may go down, you have more equipment in the path that could fail, etc… This may be a different level of concern than trying to convert a credit card machine or postage meter, etc. If your current ISP has issues maintaining your service, then perhaps you need to reconsider. You also need to consider if you have a static or dynamic public IP and if public, then you should consider static and if not possible, then get DDNS with a FQDN.
If you elect to try, then find a SIP decent provider (read the reviews) and get a new number with the service (if the existing number is not pertinent to the monitoring). Keep the existing POTS line around until such time as you are satisfied that it all works.