They certainly can. Anna University in Chennai now handles admissions to engineering colleges in Tamil Nadu following the exclusion of the Tamil Nadu Professional Colleges Entrance Examination in 2007.
For students from other states, it has a special space reserved for them, and on a different day, counseling is provided. Because there aren't many people coming from other states to study at Anna University, they should have an easy time getting in.
TNEA is the state-level admission procedure for the state of Tamil Nadu. Anna University organizes it to provide admissions to B.E./B. Tech professional degree courses. Admission will be granted solely on the basis of the intermediate (12th) class percentage. The candidate must obtain 45% (general category), 40% (backward class, including backward class Muslim), 40% (MBC and DNC), and 40% (SC/ST/SCA).