SMS verification, is it secure?

I'm going to say no. While SMS is a generally accepted 2nd factor, there have been a number of cases where an attacker has used social engineering to break into a user's carrier account and pick up the verification code and use it. So to answer your question, is it 100% secure aside from guessing, no.

EDIT: To add to this information, even NIST is removing SMS as a valid 2nd factor from their standards for security.

What you describe is absolutely not a secure approach. SMS messages are broadcast over the air without guarantee of encryption.

They can be intercepted and recorded.

In addition, your SMS messages are only as secure as your provider. Hackers can execute a social engineering attack: such as convincing a cellular carriers tech support to send messages to a device the hacker controls.

It's a public, insecure channel and should be treated as such. Adding come kind of SMS verification is better than nothing, but there are risks that may not be acceptable in the context of your application. If we are talking about authentication there are much better methods.

More:

https://www.ckn.io/blog/2015/11/29/gsm-sniffing-sms-traffic/

Of course it is not 100% secure. In addition the NIST is updating it's digital authentication guideline and is about to ban SMS.

You should use other means of 2FA when the user registers. You might even use a Smartphone App, although this sucks, too.

You will not get 100%, but if you want to get real high, you need to ship smartcards with x509 certifiactes or at least a self initialized Yubikey.