i believe yes. The quasi experiment is the type when the groups or samples are known from the beginning. E.g. you wish to compare the weight of men and women, or the SAT score in three states of USA. This is your case, at least for the first two hospitals. The third hospital makes a difference. You could also do this experiment completely at random, take these hospitals for instance and allocate the products completely at random, what you do in the third, do it in all the hospitals.