Short answer: Yes
Long answer: More or less. Heroic Finale allows the bard to give another player a free move or standard action. If the other player casts a spell that is a standard action to cast (this in the majority of spells), then they can cast it. The time to cast is specified in the spell's "Casting Time" section, under the Casting header.
Okay sounds good, but then couldn't the wizard with a bard cohort spam that all the time?
Sure, but IIRC, it's a 4th-level spell. Bards don't get a lot of spell slots, and they get them late.
Also, you have to have a Bardic Performance active (you have to end it to cast the spell). Not a huge problem- MA to start, StA to cast, and Lingering Performance if you want the benefits- just stating it for the record.