Not necessarily. The load that the healthcare systems must carry depends not just on the absolute number of cases, but also on how long the average stay in hospital
is. Think of it as IT notorious "man-days", in this case "patient-days".
If the infection is milder across the board, hospital stays will be shorter on average. People will improve faster and will be discharged sooner.
500 people who on average need 3 days of hospitalization are less of a load than 200 people who on average need 10 days of hospitalization - unless those 500 arrive at the same time, of course.