As the title says would the have been faster. Planes such as the he 112 or the bf 109-e1 or the early British spitfires or any of the American planes used in the pacific or Europe.
No. A Spitfire with swept wings would actually have been slower, unless you took it up to 30,000 feet and pointed the nose straight down - swept wings have beneficial characteristics in transonic and supersonic flight, but at lower speeds straight wings have lower drag and higher lift. That's why variable geometry or "swing-wing" aircraft (F-14, F-111, MiG-23, Su-24, Tornado, etc.) were developed, to take advantage of wing characteristics at different speeds, and why more modern aircraft intended for subsonic operation (e.g. the A-10) have straight wings. During the Second World War concerns started to surface over the loss of aircraft control at high speeds - see e.g. test pilot Eric 'Winkle' Brown's Wings On My Sleeve for work he did researching the tactical Mach number, the point at which an aircraft lost control - but prior to jet and rocket engines aircraft were only able to approach the sound barrier when diving from high altitude, hence swept wings only becoming standard in the second generation of jet fighters.
For a thorough account of aircraft wing development (up to 1978), see "[Wings: 75 years of powered flight] (https://books.google.co.uk/books?id=wc8DAAAAMBAJ&pg=PA63)" in the December 1978 issue of Popular Mechanics.