Yes, it's surely an advantage. I would say that in general, it looks good under accomplishments / experience. However, you would need to ensure that your resume is strong under academics, leadership, teamwork, impact, etc. But you probably know all this already, so instead I'll tell you something you may not know.
You mentioned that you will "most likely will not get many strategy projects as a placement student," implying that strategy is the best preparation for MBB. I don't believe strategy is the best preparation for MBB. Just look on the home page of any of MBB. Click on capabilities or services and it'll take you some time to find "strategy" because most of MBB's work is not strategy.
There are many reasons for this, but the main point is you can bring many valuable things to the table at MBB that are not experience in strategy. I spent 6.5 great years at McKinsey and didn't touch strategy. So my advice is to study the firms, figure out what you want to do there, and make your application really compelling!
Hope this helps! Happy to share more.