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No. City of Brass adds one mana of any color, and colorless is not a color.
In the past, if you attempted to add mana to your pool that did not share a color with your commander's color identity, that mana became colorless instead.
This rule was removed with the release of Oath of the Gatewatch, which introduced new colorless symbols and colorless costs.
References to special mana-generation rules for Commander are obsolete. City of Brass does what it says on the card, just like in regular Magic.
Commander rules have been updated on January 18, 2016 to make mana production work more like regular Magic.
The rationale provided says:
So, now City of Brass will just generate mana of any color (but not colorless mana) regardless of your commander's color identity.