However, once the STATE Warning Point or a National Warning Point run the tests [besides normal operability], depending on your State, County, Local policy, rules, regulations, many agencies perform a Fan-out.
When I volunteered at my EMA years ago, we were the Alt Warning Point and as part of the "Fan-Out aka Telephone TREE" we had to Call 10 other EMA Directors on the phone. The Fire Dept's used the Radio System to announce the Checker-Board test and did a roll-call.
So, No it is not Broadcast [routinely] but you might hear RELATED radio traffic being Broadcast about it.
PS, I recall a thread about this a year ot two ago, do a search on NAWAS for the thread