As a resident of Mass, I can honestly tell you it will make no difference.
The licensing authority of any city/town is the chief of police. Our Mass General Laws regarding firearms gives them "discretionary authority". That authority was meant for something like this, as well as other minor issues that could have kept someone from being issued an LTC.
However, they have abused the vagueness of the statute to cover their asses for denying an LTC to some one for absolutely no good reason (yes, it can be fought in court, it will be very expensive, and there is a very small chance of winning - because of the vagueness of the statute).
I also recommend that you look at the ATf form 4473, question 11b. If it was a felony conviction in that state, regardless of what it would have been here in Mass, that's all that matters to the feds.