Absolutely. I added this functionality to an application by creating a popup on the shape when the draw:created function fired. Here is a quick run through of how it works.
map.on('draw:created', function (e) {
var idIW = L.popup();
var content = '<span><b>Shape Name</b></span><br/><input id="shapeName" type="text"/><br/><br/><span><b>Shape Description<b/></span><br/><textarea id="shapeDesc" cols="25" rows="5"></textarea><br/><br/><input type="button" id="okBtn" value="Save" onclick="saveIdIW()"/>';
idIW.setContent(content);
idIW.setLatLng(latlng); //calculated based on the e.layertype
idIW.openOn(map);
}
function saveIdIW() {
var sName = $('#shapeName').val();
var sDesc = $('#shapeDesc').val();
var drawings = drawnItems.getLayers(); //drawnItems is a container for the drawn objects
drawings[drawings.length - 1].title = sName;
drawings[drawings.length - 1].content = sDesc;
if (idIW) {
map.closePopup();
}
}
Here is an image of how it appears:
