since you have a plan with 6 months deferral eligibility but 1 year for safe harbor it is a given that the plan is tested splitting the groups - statutory includable and otherwise excludable
the statutory includable is safe harbor so no ADP test.
the otherwise excludable most likely has no HCEs so that ADP test passes with a free ride as well.
as for your question regarding gateway minimum, again, you would probably test the a(4) portion as statutory includable and otherwise excludables.
since there would be no HCEs in the otherwise excludable group, then there would really be no test so no gateway needed.
such a plan design (different eligibility) does not have the "get out of top heavy for free card" so if the plan is top heavy, then yes they would get the 3%.
If the key employee is not receiving and nonelective contribution then the question of gateway is unimportant anyway, no matter even if the NHCEs were not otherwise excludable.