First, this has nothing to do with the creature being a "Maia" - the same will apply to Valar. "Maiar" and "Valar" are job descriptions, not races.
For all of the Ainur: Yes, in general. This does not apply to the wizards (in their time as wizards), Sauron, the balrogs, or Morgoth. In the case of the evil Ainur listed, they become tied to their physical body; in the case of the Istari, they agreed to become tied to their physical body. You should try reading the beginning of The Silmarillion. Ainur are not tied to physical bodies - they are (like you refer to them as) spirits, and can come in and out of physical shape as they wish.
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...take counsel with thyself, and remember who and what thou art.
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