If a charity is incorporated under a state’s nonprofit corporation law but is registered with other states to solicit contributions, is the organization now subject to the requirements for the Attorney General in those other states to approve certain corporate transactions, in addition to the approval that may be required from the AG in its state of incorporation?
Registration (or failure to register) in another state would ordinarily not create jurisdiction in the other state's Attorney General to pass on corporate transactions of the charity, other than those subject to the charitable solicitation registration act or those that might be criminal and are committed within the other state. Fundamental change transactions, such as amendment of articles of incorporation, sale of substantially all the assets, dissolution, conversion, etc. might require approval from the Attorney General of the home state, but would not be subject to the jurisdiction of the AG of the other state. A merger with an entity from another state might be subject to review by the AG of the other state, but only as to the action of the entity organized in that state, not as to the action of the entity that is merely registered to solicit in that state.
The general answer to this question, with caveats such as those set out above, is No, but without knowing the specific transaction that is contemplated, I am not comfortable trying to give a definitive answer.