Will you still receive text messages when you phone is off, once it's turned on?
Messages sent to the phone while it is physically turned off will be sent to the phone once it is turned back on.
There may be a limit however, to the time typically. Perhaps a week, I believe. If the phone isn't turned on after a period of time, the messages will eventually be deleted from the system.
Go to Settings
Scroll to Do Not Disturb
Select which option (manual, scheduled, exceptions[allow calls from], repeated calls off or on, then select the silence option.
Good luck.