Upon creation, will a revocable trust automatically assume the same tax exempt status as that of its creator which is an exempt entity?

A revocable trust has the tax status it is meant to have (most likely tax exempt or lessened) depending on the trustor.  Not sure what you mean by the creator of the trust and in what context the trust is created.  Trust companies are often tax exempt in some states, but the creator may be an individual who is not exempt to a corporate for profit entity that is not tax exempt.

You need to meet with your legal counsel, who should be an individual or law firm who has both extensive experience in trust creation (including various forms) but also accounting standards and tax matters.