Yes. The bigger the gap becomes, the more the economy will be geared towards serving the needs of the wealthy instead of regular people. If a trillionaire wants a mansion on Pluto or an AI to serve him, a large workforce and a lot of resources will be put towards that goal, making those resources and work more expensive to use for other goals. Your healthcare and shelter has to compete for resources and their prices will rise as the demand for overlapping resources goes up due to the huge purchasing power of the wealthy.

What we produce in this economic system is decided by money. If 90% of all money is in the hands of the wealthy, then 90% of all we make with out limited workforce and resources will be decided by them.