Log-in as service account in SQL Server Management Studio

The stored procedure that performs a CTE in production is being executed using a service account. However, the stored procedure returns empty and I tried checking this using SSMS but I my domain account has no execute functionality in production. I tried logging into SQL Server Management Studio using the service account but I ran through some problems. First was resolved by following this link - https://dba.stackexchange.com/questions/173785/the-certificate-chain-was-issued-by-an-authority-that-is-not-trusted However, once that is executed, it returns as if no user name was provided: Question is, can I login using a service account in SQL Server Management Studio?