Unfortunately yes, TCR registration is required regardless of business size or how you will be using SMS. The good news is that you will likely qualify for the low-volume conversational (UCaaS) campaign type, this will reduce the monthly fee to $1.50 per month and will cover all of your numbers. Please note the $4 brand registration (application fee) and $15 campaign vetting (application fee) still apply.
Note TCR registration is not required if your business is not currently using SMS, and not registering for TCR will not have any impact on any services outside of SMS.