Yes it does. But we don't say it that way. The picnic means a meal eaten outdoors, usually away from home (but it could be in the back yard, too). It is an event more than a location or site. We might say, "...at the picnic in the park, or the beach (wherever)" to specify a site.
Yes, "the picnic" refers to the event or occasion of having a picnic, typically outdoors. It usually implies a specific gathering where people bring food and eat together in an outdoor setting, such as a park or beach. So, it does not necessarily mean "the picnic site," but rather the overall experience of having a picnic.
"The picnic" refers to the event or gathering where people come together to eat and socialize outdoors. It can be held in various outdoor locations such as parks, beaches, or gardens. So, 'the picnic' does not specifically mean 'the picnic site', but rather the overall activity or occasion of having a meal outdoors.
