Don't decide before you get here that you can't run. Like Kero said, the pace is usually quite slow for most fighters in a gym. When we run in the morning, there's a huge gap between when the fastest runners finish and when the slowest runners catch up. It's not a race, it's what runners would call "junk miles," in that nobody cares how fast or slow you go, it's just that you're doing the work.
I am 100% in the school of thought that if you don't run, you don't Muay Thai. People who argue otherwise, to me, are making excuses. When you see two fighters in the ring, you can tell with 100% accuracy, every time, who runs and who doesn't. That said, if you literally cannot run but can do something else, like skipping or jumping on the tire for ungodly amounts of time that make up for it, that's good. It's just important that you do something. But the short and blunt answer about whether you'll be looked down on by your gym for not running: yes. How much they judge you will depend on what kind of gym it is - a western-heavy gym where lots of folks don't run, not as much - as well as if you try to make up for it with something else. If you're doing other work to make up for the run, that will be acknowledged.