TSEdCET Eligibility

Yes, you can pursue a B.Ed without giving TSEDCET 
BUT you will need to meet the eligibility criteria set by the college or university that you are applying to
becuase some universities and some colleges may have higher admission standards for students who do not give TSEDCET
you may be ask to pay more admission fees and the competition will be more intense to the admission without giving TSEDCET

here are some basic documents you will be asked for 
You must have a bachelor's degree in any discipline from a recognized university
You must have secured a minimum of 50% aggregate marks in your bachelor's degree
You must have passed the English Language Teaching Competency Test (ELTC)

Some colleges and universities may also have additional requirements, such as a minimum age requirement or a requirement to pass a personal interview so also be prepared if you are not giving TSEDCET