I would totally disencourage you from doing it.
First, consulting -particularly at the beggining,when you are still building your skillset- is very demanding in time and energy.
Secondly, companies don´t like "sharing you" -experience talking here, since I run an ONG, which was super super challenging while I was at McKinsey. I was never supported for doing so, only by some individuals-.
In a nutshell: there is plenty of time for you to do this, wait a bit and try not to put too much on your plate in an important and decisive point of your carreer.
Hope it helps!