Hello, this is a question I would ask of the music department (email/webchat etc) in the prospecting stage of your son's research, if it's high on his importance list, especially with drums vs more mainstream piano, wind/string type that the student owns.
Most unis will have music rooms. Accessibility will vary by uni, some ring-fenced for their music students, some operating booking system etc, even if the blurb says inclusive to all.
DD is just finishing freshers year, high performing musician at school but not furthering music at UG, and is the only non music student in her symphony orchestra, with many of the students filling places from the conservatoires. Her roomie is a drummer, plays in bands formed from the available societies so has gained access to practice indirectly, but admits the kit would not have been accessible without this.
All DD's peers from school have said inclusion has been limited in their respective unis, apart from those studying music. Most with their instruments untouched in their rooms after rejection at audition or lack of facilities.
On the positive, band life is good if the student is prepared to put themselves out there from the start, so I would just check in advance to avoid disappointment.