Sayyed, IIM Raipur

Yes, you can.

You can write NET exam. Management comes under course code no.17. Course code 17 include specialization includes business administration, marketing management, industrial relations and personal management. There will be two question papers paper II and paper III and paper II includes 50 objectives questions and carry 100 marks. Paper III includes have10 short essay questions carrying 16 marks and a long essay carrying 40 marks.

There is no mention that AICTE affiliated studied students are not eligible.

Candidates must have secured minimum 55% marks (without round off) in their postgraduate degree OR equivalent examination from a university or institution recognised by the UGC in Humanities (including languages) and Social Science, Computer Science & Applications, Electronic Science etc.

You can check the complete UGC NET eligibility criteria below for details.
Eligibility

Hope this helps.