Most boards start their life as a copper clad sheet. A circuit design is printed on the board and the copper that is not part of that circuit is etched away leaving the remaining copper to mount chips etc. on and keep them connected in the circuit by the conductivity of the copper. Some older boards actually gold plated the copper. So some boards actually contain gold.
On average a ton of circuit boards will contain about 300 pounds of copper. When smelting that copper provides the molten metal pool that retains the precious metals while the less desirable metals are oxidized off into the slag. Long story short, you need the copper in the smelt and the circuit boards can provide it. Otherwise you would need to add copper for the step where you generate precious metal rich slimes.