Simple answer. No.

Complex answer. A MTA (Mail Transfer Agent) is needed that supports integration with bulk SMS services by a cellular network provider. Something that needs to be purchased and integrated.

There are no magics and potions that can turn a SMTP conversation (mail client talking to mail server via SMTP) into a SMS.

Our Lotus Notes system (don't ask it's nothing to do with me!) is set up for our email and also to send out SMS'.
For our database applications to send out SMS' we just send an email using UTL_MAIL (or you can use UTL_SMTP) to the mail server (on Lotus Notes) which then sends it via SMS.
As Billy says, it depends on your own setup, but in general, no the database itself cannot send SMS messages, but it's possible to do it via other 3rd party products.

If it is not clear I can add something more as I'm a bit experienced in telecom.
Oracle does not provide a way to send SMS because an SMS has to be sent (eventually) by a mobile phone operator which can be reached via an SMS gateway or a GSM device.
To answer also at another question you put in a another post, SMSs are not free, they are not email and mobile phone operators charge for sending them.

You can find some few sites which allow to send few SMSs per day for free but in general to send a large quantity of SMS you have to pay for them.