Going to a tech firm in a role of your choice is less about where you get in from : MBB or Tier 2. Its more about the type of work and experience you pick up where you are NOW or at the point of making the move to tech firm. Trust me, most tech firms don't really care too much where you come firm (Yes, a MBB brand might get you that interview, but thats about it)- they need people will hands on delivery skills to roll up their skills and deliver tangible products/services.
So join MBB if its going to give you the skills/experience needed to land that job in tech.