It will, as an R higher than 1 means that there will be no maximum in the new infections at all (while any health system obviously does have a maximum capacity

It will, as an R higher than 1 means that there will be no maximum in the new infections at all (while any health system obviously does have a maximum capacity that is significantly lower than the size of the population). R going lower than one means, there will be a maximum in the future. Of course, only when numbers are currently increasing. R is basically the second derivation of the case count (+1). So a lower R first means that the increase in new infections decreases, until the new infections decrease.