No.
That is not a valid basis for objection to the admission of the letter. The letter says what it says. It might be evidence for a possible attempted extortion or witness intimidation sort of charge. If it is, not admitting it in your disorderly conduct case would not change that. You have the option not to testify in the disorderly conduct case. But if you do, one of the concerns would be that you might say something that would make things worse. Indeed, that very risk is why in most cases criminal defense attorneys counsel their clients not to testify. You have to decide if the potential benefits from testimony will outweigh the risks. None of that, though, affects whether the letter itself is admissible.
The letter itself does not appear to amount to the crime of attempted extortion, which is what the crime is called in Massachusetts. That crime requires that you make a threat to accuse someone of a crime or threaten some kind of injury to the other person. It could be used in addition to some other evidence, however, to prove attempted extortion. Just doesn’t strike me as enough on its own to meet the requirements of the crime.
But it might be considered witness intimidation.
For a variety of reasons that letter really never should have been sent, especially not while criminal charges relating to the incident are pending against you. You seem to have the impulse to lash out at others whom you think have somehow offended you. Acting on that kind of impulse, in my experience, doesn’t make anything better and often leads to more trouble. I suggest that you refrain from further contacting the business or its attorney while this criminal case is pending. At the very least, I think it best not to send any more letters remotely like that earlier one.