Yes it can. Text messages can be sent using email programs and Total Access Emailer for Microsoft Access is capable of sending text messages to your recipients. To send a text message via email, you must simply use the SMS Text to Email gateway that is determined by the recipients provider.
This is done my determining the convention required for the "TO" address that you will be using to send the email as a text message to a given recipient. This format varies by provider.
For example, for AT&T recipients, the SMS email convention uses this:
Where "number" is the cell phone number of the recipient.
The following URL provides some examples of other SMS gateway formats that are required by other popular providers.
If the one that you are looking for is not listed, you may locate it by simply performing a search on the web or by contacting the provider directly. If you're given a number, and you don't know what the mobile provider is, you can use this site to determine that: