Not according to the guard I spoke to at the entrance and from what you can observe with your own eyes. Additionally, with the Beach Club being closer to Epcot than the BW, why does The BW have all the parking problems and the Beach Club doesn't? The reason is that if you don't have a confirmed ADR, or are a registered guest of the Beach Club, they won't let you park there. Compare that to the BW, where sometimes the parking can be a horror show. Just read the previous numerous posts complaining about the BW parking to see how widespread the problem is.
The sign restricting parking at the BW is basically meaningless- go on the Boardwalk after 9pm when Epcot closes, and you can get run over by all the people going leaving the park and then going to their cars in the BW lot. Check the parking lot close to 10pm and you will see that it is usually half full.
The only way to effectively control the parking at the BW is to install a gate (by the convention center) that you can access only with your magic band. This will guarantee that if you are a resort guest you will get a spot to park, never mind that driving around for half an hour looking for a spot is ridiculous, especially when WDW is now charging guest $25 to park their car overnight. Park in the lot to the left of the guard shack or valet if you are not a registered guest, don't use the lot by the convention center.
Agreed that they may be more strict during Food & Wine, but generally speaking the people who are in charge of parking at the BW need to give their head a shake.