Can a Diploma student do engineering in your college?

Yes, a Diploma student can do Engineering in College of Engineering- Anna University (CEG, Guindy) for BE in Industrial Engineering.

I guess you can get a seat in affiliated colleges, but not here.

Hello Malashree, A Diploma holder can surely seek admission under lateral admission scheme in his/her her state. Each state has devised a scheme. I think in TN also you can seek admission based on your marks of Diploma.