Yes, you can do it.
You need to disable your 2FA then enable SMS verification method.
Step 1: Disable 2FA
Gear icon --> Setup --> Security --> Session Settings --> Session Security Levels.
Right-hand Side multi-select column Select Two Factor Authentication and click Remove button.
Step 2: Enable SMS Verification
Gear icon --> Setup --> ...
I would like to shed some light here since it has been a couple of days without any comments or answers.
I went through the documentation and help pages and found nothing regarding blackout period specifically for SMS sends using Transactional API, however, there is a little note in the blackout period doc:
Any send blackout time specified in the ...