The same applies to takeoff. If the SID requires a climb gradient higher than the OEI capability,(due to obstacles) we can still accept that SID as long as we have an engine-out procedure. It does not mean that we cannot fly that SID at all.
However, if the higher climb gradient is not related to obstacle clearance, then an engine-out SID is not necessary — for example, if it is required for noise abatement or due to ATC requirements.