Sim, você deve instalar capas nas caixas.
Você deve conseguir capas no hardware local ou na caixa grande, razoavelmente barato. Apenas certifique-se de medir todas as caixas e anote sua forma antes de ir para a loja. Se os parafusos de montagem não estiverem nas caixas, você também terá que pegar alguns deles.
National Electrical Code 2014
Chapter 3 Wiring Methods
Article 314 Outlet, Device, Pull, and Junction Boxes; Conduit Bodies; Fittings; and Handhole Enclosures.
314.25 Covers and Canopies. In completed installations, each box shall have a cover, faceplate, lampholder, or luminaire canopy, except where the installation complies with 410.24(B). Screws used for the purpose of attaching covers, or other equipment to the box, shall be either machine screws matching the thread gage or size that is integral to the box or in accordance with the manufacturer’s instructions.
Não, você não pode cobrir as caixas com o drywall. As caixas devem permanecer acessíveis.
314.29 Boxes, Conduit Bodies, and Handhole Enclosures to Be Accessible. Boxes, conduit bodies, and handhole enclosures shall be installed so that the wiring contained in them can be rendered accessible without removing any part of the building or structure, or, in underground circuits, without excavating sidewalks, paving, earth, or other substance that is to be used to establish the finished grade.