Yes, if they have people working for them other than as employees of contractors or other companies.  The homeowner's association is a legal entity, a "person," and is subject to the Workers' Compensation statutes, as well as most other laws, on the same basis as any other person or business.

Workers compensation is actually a good deal for employers.  Compared to a fault-lawsuit-based system, compensation is far simpler to determine and much less costly, for workplace injuries.