Short answer is yes.
But not for the reasons you might think. Everyone knows you will use software/calculators to do modelling/maths once in IB.
However, multiple aspects why it is important. Spot checking your analyses ex-post (for quality assurance), simulating impact on figures ex-ante (i.e. before you updated the model, what do you expect the result to change). However, most importantly, senior Banker / client interaction. Mental maths gives you flexibility to play through ad-hoc scenarios with clients on the spot.
Hence, mental math is an important QA and client-service tool.