No. If you cast a spell due to madness, that doesn't affect any additional costs that may or must be paid (C.R. 118.9, 118.9d, 702.34a), such as the "commander tax" under C.R. 903.8. Generally, all that differs when paying for a spell due to madness is that the spell's mana cost is not paid (C.R. 702.34a). See also this thread.
Just to be clear, when you cast a spell using madness, you're still casting it, which means any appropriate additional costs must still be paid. The madness alternative cost only replaces the mana cost (which is only what's printed in the upper corner of the card).
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I'm a former judge (lapsed), who keeps up to date on rules and policy. Keep in mind that judges' answers aren't necessarily more valid than those of people who aren't judges; what matters is we can quote the rules to back up our answers. When in doubt, ask for such quotes.
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Madness and tax effects?