Irelia ability must resolve to get +1

Yes — Irelia, Fervent only gets +1 if her own triggered ability resolves.

The +1 is a triggered ability placed on the Chain the moment she is chosen (at finalization) or readied. It resolves independently: if the spell that chose her is countered afterward, the trigger is already on the Chain and still resolves, giving her +1 (FAQ #5762, #9163). But if the trigger itself is countered or removed before resolving, she gets nothing — the trigger must complete to grant the +1.