If the Sheriff can charge (per firearm) they might just go for it....
The fun part will be in their finding time and personnel to do the paperwork.
Not to mention you can't bring a firearm into the Sheriff's Office.
The bolded is exactly why NC still has a Pistol Purchase Permit system. Every time the topic comes up, its vehemently opposed by the NC sheriffs who make money on the process.
For the unfamiliar, in NC you need either a pistol purchase permit or concealed carry license in order to purchase a pistol in the state (whether FFL or private sale). It stems from the Jim Crow era as a mechanism by which a sheriff could deny a permit (and thus 2A rights) to the "wrong" people.
The repeal has been brought up several times, but due to political opposition from the sheriffs, has never passed...
Having witnessed that occur when I lived there, I'd be far more interested in what informed citizens of OH think of the legislation than what the sheriffs themselves think.
(I should point out that based on my interactions, the opposition to repeal was not necessarily the opinion of NC law enforcement... just the elected sheriffs)