Leejor pointed out one of the biggest challenges -- the caller might not be on a cell phone. The second challenge is where customer replies go?
3CX is working on integrating SMS into the PBX but it is not released yet. When they do release SMS capabilities (hopefully soon) we will presumably have more options for direct integration.
Regardless of what 3CX does in the future, your SIP provider may provide SMS capabilities today. It is not uncommon, for example, for carriers to provide an email to SMS gateway you can use to send outbound texts simply by sending an email to <phone-number>@<my-SIP-carrier>.com. The body of the email is converted to text and sent out as SMS to the phone number specified in the email address.
A server-side application could be written to watch for missed calls and send the appropriate email (SMS text). Depending on the capabilities of your carrier, you could either validate the phone number is associated with a cell phone prior to sending the email, or they may just ignore requests sent to a number that is not associated with a cell phone.
When / If the customer replies, we could have a web application subscribe to SMS events generated by your carrier. The web application (via popup) could notify you of a new incoming text. In the web application you could see and respond to inbound texts.
How much of this solution you need to build and how much may be provided by 3CX in the future is unclear, but it absolutely is possible today regardless of what 3CX chooses to implement. I should point out that it is very rare that someone asks for a new feature that cannot be implemented either natively in 3CX or through custom programming. The real challenge, almost always, is coming up with adequate funding when custom development is required.