Do you mean, as in .... a one-room county school-house? Not sure about Louisianna, but here in CA 1-room school house sites are often un-productive. I've hunted scores of such sites that we knew for a fact were virgin (found rivots, levi buttons, lantern parts, etc... ), yet not many coins, if any at all. In rural areas here, it seemed that prior to the age of bussing ('20s and '30s) there were 1-room school houses every 5 miles along all country roads. So scores of such spots exist. Yet they rarely pork out coins.
A little deeper sleuthing revealed why: There'd sometimes be a few as a dozen kids, and sometimes existing for as little as 4 or 5 years. Perhaps 15 or 20 at the most. And if, for example, it existed from 1890 to 1940 (a VERY long lived one), invariably any coin we'd find would be at the later end of that spectrum (a '39 wheatie, for instance). Because it wasn't till after WWII that America entered into such a prosperous time, that kids were carrying coin $ to school, to begin with. This same trend is seen in the demographics of finds from urban schools too: So for example, if there's an inner city urban elementary school blt. in 1920, and you were to talk to someone who's gotten 1000's of coins from there (because perhaps they started detecting it in the 1970s when things were virgin), they would concur that the vast amount of silver and wheaties post-date WWII as for time-when-lost. So if there's teens coins found, they're more worn d/t lost later. At first, back in those days, we wrote that off to the fact that the "older coins must be deeper". But eventually came to see, that that's just how the demographics worked. In the 1950s school lunch programs started, milk for the 5c or 10c, and so forth. So there came a time when every kid had coins in his pocket. Not true of the '30s and earlier kids. ESPECIALLY rural areas.
Exceptions in productivity will be if the school house were also used for adult activities. Ie.: grange halls, churches-on-Sunday, and so forth.
But by all means, try it. Ya never know.
