Yes, you can become an engineer after entering NDA.

You have to select Army or Naval academy which gives an option to study engineering, if you take airforce they are more into pilot training.

There is also a technical entry for the army after 10+2, clearing which you can get into technical field. Training will be in OTA Gaya.

One more option is to do engineering from any private or government college, then write IES( Indian Engineering Services ) Exam, if you come in merit you can become a gazetted officer.

or

SSC Junior Engineer exam from which you can join defense engineering department.

Also in the last year or after graduation, you have a lot of entries such as UES(University Entry Scheme), SSC tech entry, TGC entry, AFCAT, CDS.

Many ways are there provided you get well prepared because it will be one of the toughest selection procedures.