Q: Do cards drawn as part of Draw 3, Play 2 of them count towards the Goal 10 Cards In Hand?

A: No. You have set your main hand aside, and cards drawn as part of Draw 3 Play 2 of Them (or Draw 2 and Use ‘Em) are not considered part of your actual hand. They exist in an alternate temporary mini-hand dimension.

The same is true of the cards drawn as part of utilizing Goal Bonanza. Those cards which you draw and must immediately use are not considered part of your “main hand.”