Definitely runnable without it.

I've only played Mothership for a oneshot (over multiple sessions) while waiting on a party member to become available.

We did not have TT/VTT. We had some visual aids, like the layouts of ships were sent in chat for us to look at. I don't think it really hampered the experience, and I have aphantasia so "theater of the mind" usually doesn't help me much lol. It was more than serviceable.

I've run a small campaign of mother ship and a one shot. I didn't use any visual aids other than a map of the space station as a handout. No issues whatsoever so it should be totally fine to run theatre or the mind.

I played it with some friends. There's an app you can get on your phone for character sheets and you don't even need that if you prefer pen and paper.

I haven't played it but in general to me the rules seem rather in the OSR direction, so I feel there's nothing in the rules that would necessitate a VTT.

Also, there's https://www.owlbear.rodeo/ it's browser based and if you can fit under 50M per image it's free. I would guess a device would sooner have problems with zoom than this. One of our players does use mobile with owlbear.

I've run a dozen sessions of Mothership and never used any kind of minis or tokens to track movement.

I do highly recommend the official mobile app though as it has a character sheet tracker and dice roller and can join people together in a game session.