No.
You will not be able to do this. If the SenderID is not relevant or does not reflect your company’s brand name, it will be rejected. Similarly, if the template does not have your company’s brand name, this template will not be approved.
This is the reason why registration was made mandatory by TRAI for all companies, on the DLT portals. With this direct registration method, tracking, regulating, and holding the entities/companies accountable for any and all content triggered from their registered details has become easier.