No, pregnancy will not cause your application to be rejected, as long as you’re enrolling in an employer-sponsored group health plan or an ACA-compliant individual/family health plan. The ACA prohibits health plans from turning away applicants because of preexisting conditions, including pregnancy.
Prior to 2014, pregnant women (and expectant fathers) in most states could not obtain coverage in the individual/family market, even if the plan didn’t include any maternity benefits (the reason expectant fathers were denied coverage was that insurers were generally required to allow either parent to add a newborn baby to the parent’s existing health policy without any medical underwriting; allowing either parent to enroll during the pregnancy would open the insurer up to potentially having to cover a baby with serious health conditions from the first day of its life).