Hello Sage,
Yes, you should check any relevant firewalls, including software firewalls on your server.
If you have shell access on your WordPress machine, you can also use nc to check if the RPC port on the wallet server is reachable.
If the wallet server is down, then attempts to communicate with its RPC port will likely fail immediately, rather than timeout. The plugin can handle this without crashing. Only the coin on that wallet should become unavailable in the frontend UIs. If you plan to keep the server down for a while, you can deactivate the coin adapter just to be sure.
If you have any more questions please open a new thread.
with regards
P.S. In the upcoming wallets6 release, this behavior will change. Wallets will be decoupled from currencies, and therefore a currency will still be usable if the wallet is offline. Only deposits/withdrawals will obviously stop for as long as the wallet is offline.