So in the case of Instill Bravery (Once a round when an investigator is to lose sanity...prevent up to 2) I could
Yes. Think of it this way: All delayed does is make you have 0 actions that turn. In a normal round you would often have already spent your actions when you cast Instill Bravery, so you would have 0 actions and still be allowed to cast spells, as long as they do not say Action.
Other side note: Nothing keeps you from using them to reduce any health/SAN consequences from other spells, so they are powerful spellcasting tools.
(Experience from other games, especially RPGs, where spell drain and the such is often hard/impossible to heal may contaminate judgement on this, nothing indicates that similar would be the case in EH, it's just loss like any other.)