Although wouldn't the duration card still have to be out to get it's bonus? Or could you procession a hireling and draw infinite cards?
ConMan kind of explained this, but i'll still answer this directly:
No to the first question. Yes to the second.
The reason is that any effect that is not below a dividing line is set up as soon as you play a card, and what happens to the card later is not of relevance. This is a bit confusing with Durations at first, but their effects are not conceptionally different from Smithies +3 Cards in that regard. Such an effect may be timed for later, like Scheme or Coppersmith, or have implicit conditions, like Champion. But the effect itself is set up as soon as the card is played.
This is different to effects that are inherently dependant on a condition, like "while in play", "when you trash this", "when you gain this" and reaction effects. All of those are below a dividing line to show that their effect is different from "on play" effects, and is not set up on playing a card.
A well known example for this is that playing
Bridge twice with Throne Room actually reduces costs by
(effect is above the line), while using Throne Room on
Highway draws and gives actions twice (above), but only reduces costs by
.
Similarly, a Processed Monument will give you +2
, a processed Goons none, no matter how much you buy.
Hope this helps.