Using the AMPscript within the email body to send SMS is possible but it is not easy to setup as you would need Triggered SMS and API call to triggered SMS.
According to your situation, the easiest way you would send a sms setting up an outbound sms in MobileConnect where you would select template type as
Outbound - Automation. Activate the Outbound Message in MobileConnect thus allowing you to use the
Send SMS activity in Automation Studio.
Note: You will need to create the list in MobileConnect to be able to
setup an Outbound sms.
Yes, most of the AMPscript functions can be used within the MobileConnect app. However depending on the complexity (personalisation,report,send-log,etc) of the sms message AMPscript use case can vary.
Here is an example:
Hi %%First_Name%%, this is a sms test.
Above case uses
First_Name as the personalisation string which matches with the field in the list setup in MobileConnect. However, if you need to lookup further fields in the DE then you will need to use LookUp AMPscript functions.