Hi Brandon,
This is totally doable with FreeSWITCH. For you I recommend starting small and working your way up. What I mean by that is that you should probably get the basics down first, like learning how to do a simple dialplan entry in FreeSWITCH, how to set up a SIP provider, how to set up a TTS engine like svox/pico or a commercial one like Cepstral, how to do an originate on the command line and then how to script that using something simple (like fs_cli -x 'originate foo/bar') or more in depth (like ESL)...
Then there are the other questions, like:
How do you get the patient information out of the software? Is there an API?
Will you be keeping track of the results of your automated outbound calls?
If so, how will you get the results back into the software? Will you auto-reschedule busy/no answer calls?
Do you want to leave a simple message with the called party even if a human answers?
Or do you want to have a simple IVR that says something like: "you have an appointment at [date/time]. press 1 to confirm. if you need to reschedule, press 2."?
Will you want answering machine detection? If so you'll need to contact FreeSWITCH Solutions about purchasing a license since this is not a free module.
Last question: what programming skills do you have on staff there? If you have basic shell scripting skills and/or Perl/PHP/Python/etc. skills then you can probably build something yourself. If you don't have someone with some programming skills then I strongly recommend that you find or hire someone to assist. It's not impossible for a determined person to learn all the skills required, however it will be a challenge.
Hope this helps!
-Michael
P.S. here is a really, really simple example of how to make an outbound call from a shell script:
#!/bin/bash
# simple dialout script, assumes a gateway named 'flowroute'
# and syntax: dialout.sh <phonenumber> <firstname> <lastname> <appt_timestamp>
res=`fs_cli -x '{ignore_early_media=true,fname=$2,lname=$3,appt_timestamp=$4}sofia/gateway/flowroute/$1 reminder`
Call that script from shell using a Unix timestamp for the appointment date/time, like this:
Then have a simple dialplan (assumes you've built one of the TTS engines):
<condition field="destination_number" expression="^reminder$">
<action application="answer"/>
<action application="sleep" data="1000"/> <!-- pause for a sec, let media kick in -->
<action application="playback" data="this_is_a_message_for.wav"/>
<action application="speak" data="${fname} ${lname}"/>
<action application="playback" data="you_have_an_appointment_on.wav"/>
<action application="say" data="en short_date_time pronounced ${appt_timestamp}"/>
<action application="playback" data="please_dont_miss_or_we_charge_obnoxious_fee.wav"/>
<action application="hangup"/>
</condition>
</extension>