No

I concur with Gray. Concur is also a very advanced English word, which I can say that I very seldom use, and I've written scientific reports and papers for very big companies in the UK. There is nothing wrong with using the word "agree". There is also nothing wrong with practice, and using the word can be fun. If so... go ahead and follow the advice given by Gray.

'Concur' is mostly used intransitively, and reflects opinions. One doesn't 'concur to do' something. We use it to agree with a statement or proposition. You can 'concur that' something is true/right/correct. Or 'Concur with smb. on smth' From your example, you could say 'Staff did not concur with the proposed change in date being a good idea'

No, because "to concur" means "to agree in opinion" (i.e. to have the same opinion). It doesn't mean "to agree" in the sense of agreeing to do something. You could say "The staff concurred that it would be best to change the date." In this case, you are saying that the staff members share an opinion (probably with someone else, such as their boss), and the shared opinion is that it is best to change the date. "I concur that the movie is terrible" = "I agree with your opinion that the movie is terrible." After "concur," you will usually use either the word "with" (to indicate the person whose opinion you agree with -- "I concur with you") or "that" (to indicate what opinion you agree with). (Edit: Sorry, I somehow missed that your sentence was a negation. Benjamin has given a good option for using "concur" in the negative.)