The Presto itself won't directly interfere with the medical alert system. Both can co-exist peacefully.  The only chance there could be a conflict is if the medical alert system is activated at the exact time Presto is checking for new messages, in which the line will be in use. However, you can specify what time the Presto will dial in to check for new mail and the chance for conflict is greatly reduced if you only check for messages once per day.

Also, if the medical alert system tries to grab the line whiel the Presto is in operation, the Presto should terminate its connection and free the line fairly quickly. So in the slim chance Presto and alert system both go for the line, Presto will hang up and the alert system can be restarted and will connect on the second try.  

Worse comes to worse, you could always get a second dedicated line to the alert system to guarantee it always has access to a phone line. 

Hope that helps. 

Mind Over Matt'er - Technology musings, opinion, and more straight from TechLore's head geek.