Not that it should, mind. But I could imagine it causing problems and not being a good explanation for an officer’s response to a situation in a tight space.
Police academy instructor here. All recruits must undergo a psychological examination before being hired. I’ve never heard of claustrophobia being a disqualifier. On the other hand, I’ve never even seen it mentioned on a report. I did hear of an applicant that admitted to a phobia of firearms. As in, panic-stricken in their presence. He failed the exam. Why even apply?
It’s going on 30 years since I took the psych test. My memory is incomplete but I don’t remember any questions about claustrophobia. I also don’t remember any possible claustrophobic episodes during my career.
I’ve taken several psych tests over the last 41 years. Even working part-time on a township lake patrol requires them per state law. Many of the tests were different from each other. None of them said anything about claustrophobia.
During my first career as a Sheriffs Deputy if you got assigned to the jail you’d have to ocassionally go into pods and toss cells (seach for contraband). I knew a couple of Deps that hated going into the cells as their claustrophobia would kick in. Don’t know of anyone whose career ended because of it.
I got assigned to the county zoo once, a premium gig almost as good as working the airport. I worked with a female Deputy. After a couple of weeks together she told me that if anything ever went down I would have to handle it as she could never point a firearm at an actual person and she could never shoot anyone. I wrote up a report regarding that and made a statement to IA. She ended up working the last 6 years of her career in the jail (worst assignment EVER) where even though she had to maintain certification in firearms she never actually carried one there. She also refused to talk to me ever again. Tough shit. I’m not working with someone who won’t use force when it’s justified. I like to go home at the end of my shift.
Years ago I rented such a small apartment that when I called the police for a noisy neighbor complaint, one of the officers said he couldn’t come inside because he was claustrophobic.
How about fear of heights? Vertigo. 
Seriously, how often do cops have to jump between buildings? “He got away” is a perfectly valid report.
Isn’t it the criminals who are hiding from the police that usually end up in claustrophobic places - in the boat under a tarp, under the bed, in a closet, in the attic, etc?