Like much Elizabethan drama (King Lear being a prime example) the subplot of Volpone was quite important. The subplot often reintroduces themes previously addressed and casts them in a new light, allowing the audience to reflect on their importance.
Things are a bit different in Johnson's play, as typically main characters in the earlier portions are also involved in the subplot: not so here. In Act II's introduction of the subplot, the audience is introduced to Sir Politic, Lady Politic and Peregrine. These now-key players have had almost nothing to do with the earlier Act.
One thing the two acts do have in common is the emphasis on gullibility and greed. The subplot also satirizes vanity. Without the subplot, these vices may not have been as fully realized, for one bounces off the other and reflects, like a mirror, brightly lit and showing every flaw.