Does Urza, Lord High Artificer let you tap mana rocks for extra mana on top of their normal production?
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The short answer
No, Urza doesn't generate extra mana beyond what your artifacts would normally produce. Instead, his ability lets you redirect untapped artifacts to produce blue mana instead of their normal mana. You're choosing how each artifact taps each turn, not adding an extra tap to the same artifact. The power of Urza comes from the flexibility and blue mana fixing, not from doubling your artifact mana.
The card
Urza, Lord High Artificer
When Urza enters, create a 0/0 colorless Construct artifact creature token with "This token gets +1/+1 for each artifact you control."
Tap an untapped artifact you control: Add .
: Shuffle your library, then exile the top card. Until end of turn, you may play that card without paying its mana cost.