in theory you can do that, however , as there would be carrier costs involved, there is no generic way to implement something that does that (as – depending on where you are – prices and options will differ)

having said that , there are a lot of email 2 sms providers out there you can choose from which should easily allow you to set this up (which one works for you is something for you to decide though as it would depend on your location etc)

furthermore, IF you were to do that you should consider the following.
SMS has a character limit per message, so if you have a large order and want to send the whole order as sms to the customer, it will be a multi-part message (with multiple message charges to you !!)

secondly, in todays world of smartphones , more and more people will have email on their phone anyway…..(not everyone of course)

Either way, just my 2 cents really