Hello

YES ! , PG admissions in Engineering Institutions are done on the basis of GATE scores, followed by written test/interview(in most of the IITs). But in NITs it is done only on the basis of GATE scores. If your GATE is in ECE then you are eligible for M Tech admissions in ECE. GATE does not prohibit an EE graduate from writing GATE examination in ECE.

But as you mentioned a particular University then you have to ask them because some of the universities does not allow these system.