Is a data science internship okay to take before recruiting for management consulting full-time?

Some context: I'm a 3rd year engineering student in Canada that has an offer for data science at one of the big Canadian banks for my junior year internship. However, I want to recruit for management consulting (particularly MBB/T2/B4) for full-time. The position is less data analysis and more so predictive modelling - high opportunity for impact at this internship, which is attractive to me.

Is data science a good internship to take to recruit for management consulting full-time? Am I pigeon-holing myself too much as an "engineer" and not a consultant by doing this, in your opinion? Will my story be too hard of a sell coming out of a data science internship?

I want to go with this data science offer for an internship because I feel like it might be a useful skill set (even in consulting) and provides a viable back up career in case I strike out in consulting recruitment full-time. Wish I could go through consulting recruitment as well for the summer, but I have to accept this offer well before interviews occur in Canada.

As for the rest of my profile, GPA is very strong and well rounded resume - variety of leadership positions and EC's. Past internship experience in a more soft skills oriented environment at Deloitte in advisory.

Any insight in guidance is appreciated! I have an interview for an analogous role (data science) for a larger brand name (think P&G/Unilever/Nestle) but interviews are after this offer explodes (and this internship I have in hand looks to be higher impact).

Tl;dr --> engineering major, past internship at Deloitte in advisory (not S&O), data science internship offer on the table. Concerned that a technical internship in data science will not be good for MBB et al.