You can easily check if a server is on the Mojang server blacklist. If a server is on the blacklist, players will be unable to join.
A request could look something like this to see if Arkham Network is blocked:
To try this API, click the button on the right:
JSON response will be shown here
Most of the response is self-explanatory, the lastUpdate value is when we last fetched the blacklist from Mojang. We do this in the background once per hour.
Cache information is sent in the HTTP headers, which are explained here.