hi,

yes you can join merchant navy after b.tech in mechanical engineering.  as mechanical and marine engineering has many subjects in common that will be easier for you to do this course.

you can do 1 year Graduate Marine Engineering (GME) course after mechanical engineering   to enter merchant navy.

however select the college according where placement is really good.

some institute offers this course:

Hindustan Institute of Maritime Training

Maritime Foundation

Coimbatore Marine Centre

Vels University

Training Ship Rahaman

C.V. Raman College of Engineering

Vishwakarma Maritime Institute

Mangalore Marine Institute