No. City of Brass adds one mana of any color, and colorless is not a color.
105.4. If a player is asked to choose a color, he or she must choose one of the five colors. “Multicolored” is not a color. Neither is “colorless.”
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.
Rule 4. If a player would produce mana of colors that are not in their General card's color identity, they instead get that much colorless mana.
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.
- Rule 4 (mana generation restriction) is removed
The rationale provided says:
Being able to generate colorless mana more easily in Commander wasn't going to break anything. But, it represented another "gotcha" moment for players, who were now likely to learn about Rule 4 when someone exploited the colorless loophole. We could paper over it (both "mana generated from off-color sources can only pay generic costs" and "you can't pay a cost outside your color identity" were considered), but a lot of the flavor would be lost in the transition, defeating the purpose. Without the resonant flavor, Rule 4 was increasingly looking like mana burn - a rule that didn't come up enough to justify it's existence.
So, now City of Brass will just generate mana of any color (but not colorless mana) regardless of your commander's color identity.