Is inverted word order such as "Anybody else does have any other concerns?" correct?

Anybody else does have any other concerns?

To my mind it is not clear whether this sentence is a statement or a question:

• If it's intended to be a statement, then the use of "Anybody" is incorrect, because that implies a question, so it should be something like:

  
  
  

  
  

  Somebody else does have (some) other concerns
  I do have other concerns

  
  




• If, on the other hand, it is intended to be a question, then the use of "anybody" is correct, but the subject-verb word order is wrong for a question and should be reversed. Hence your alternative version is fine:

  
  
  

  
  

  Does anybody else have any other concerns?

  
  

Summarising, if I were reading / hearing the sentence:

Anybody else does have any other concerns?

I would not know whether you were asking a question or making a statement, because the word order suggests a statement, but the use of "anybody" suggests a question.