I was a little down on this card after Peter Sylvester came out because I think he is a far better ally for Agnes (or Jim for that matter!) than Arcane Initiate and I wouldn't want them to compete for the same ally slot. But then I considered the following- Would I play a 1-resource event that allowed me to search the top three cards of my deck for a spell and prevent the next damage or two horror? Yes. Yes I would, that is an insane amount of value for an action card. I no longer think about Arcane Initiate as competing for an ally slot. She gets one or two activations and then protects me from an attack or something. As long as you're planning on killing her off, the doom counter is manageable and free spell draws is (almost) always good.
Obviously, the above evaluation is a little short sighted. There will be times where playing her is restrictive due to doom or when you already have Peter Sylvester and can't afford to throw him away for one or two activations of Arcane Initiate. But I still think she is worth including in any spell deck. Hitting on it once pays for itself. I recommend you mulligan for her over your "better" ally in your opening hand, getting the value out of her and dumping her at your earliest convenience when you can than play out your Peter or what have you.