I think students these days want information right away and are used to texting their family and friends and even their bosses. If the text is used to say they are going to be late, or have a quick questions on the assignment than I think it is fine. However, my University prohibits texting with students so I do not encourage it. The only issue I can see is that students need boundaries and understand that you cannot always get back to them instantly. I think a quick text telling me they sent me an email would be great as it would encourage me to check the email quicker than normal so that I can help the student with their questions.
Debra,
I work with people who definitely allow their students to text them and they text students reminders just as they would do in an LMS through an announcement. Communication is the key - however it might work for you!