Can drone pilots call 1-800-WX-BRIEF to get weather information like pilots of crewed aircraft can?
Yes, that is a general FAA-related resource. The site is less helpful. If calling - know your lingo.
But there are many better resources for drone flight management. B4UFly and a good weather app are all I generally use. I found the reference cited antiquated, difficult to use, and not as helpful as basic weather-tracking tools.
In general, I recommend a hard skip on that resource.