Texted invitations will not show in your Evite account until you submit your RSVP with the same email address registered to your Evite account.
When you go to submit your RSVP, you will be required to enter an email address. As long as that email address is the same as what is registered to your account, you can then access the event from your account.
Registering your phone number to Evite will not make the invitation appear on your account before RSVPing.