Of course it will work without shortening the existing chain, but I'd always run a new chain with a new cassette, otherwise you're just accelerating the wear of the new component until it syncs it the spacing of the old component(s). The shifting can also be a bit glitchy while it syncs in.
Since chains wear out fastest you'd be wearing out two cassettes and the chainrings even faster if you just use one chain because the wear is bound to be uneven between the cassettes particularly if you mostly use only a handful of the smaller sprockets on the commute. A straighter block would mean you would probably use more sprockets slowing down the chain wear.
Of course the real answer is another bike!