Yes you can use a starter check to pay rent, bills and much more.
The starter check is a real check that has your bank account number and routing number on it so the check is a real check but it just doesn't have your name or address on the check.
You can send a starter check as a rent payment as long as you have the money in the bank to cover the check that is written out for the rent payment.
Some landlords might want your name and address on the check to make it easier to track but I've had no issues with sending a starter check to pay rent before.
I've also used starter checks to pay for bills such as my electric bill and the starter check went through just fine.