Do you think the halfpenny would be worth getting authenticated?
In order to answer your question, you would first have to understand the differences between a colonial counterfeit halfpenny, a british counterfeit halfpenny, and a regal (genuine) halfpenny. You would have to understand what makes each category collectible in its own regard.
I already told you that yours is NOT a colonial (Machin's Mills) counterfeit halfpenny. This is the most desirable and valuable of the categories. That leaves british counterfeit or regal. In its current condition, regal would be the least valuable as it would not appeal to your run of the mill world coin collectors. It would never be "slab-able" without a details grade and thus, fairly low valued.
I strongly believe it to be a british counterfeit, which would make this coin collectible to specialty collectors but probably not collectible to run of the mill collectors (because all counterfeits are bad, right?).
So, given that explanation, I ask, what would be the purpose of having it authenticated?
If you really want to know more about it, post some CLEAR pictures of the date. I can tell you that I paid $150 for a british counterfeit that would be described as problem free AU (some might even call it UNC). Yours might be worth $20-50 on a good day.
EDIT: Your coin is dated 1773 and is in the british counterfeit "family" known as "Aging George".