Generally, acute care experience is accrued inside the walls of an acute care hospital. Urgent care centers are wonderful places to build assessment and procedural skills, but it is not acute care experience.
I had worked at a small community acute care hospital that only had an urgent care and not an ER. Since it is within a hospital setting that particular case it would be considered acute. But there are plenty of urgent care sites that are not associated with a hospital (stand alone) and I believe those would not be considered acute.
Despite that, I think if you were looking to work at a hospital setting, urgent care can still provide a good experience like triaging and patient care.