A decent mixdown is necessary for your demo to be considered by most labels, I would say. Having a good master for your demo is probably preferred (less work for them), but it might not be necessary. I would at the very least send a demo with some kind of rough master, just to better show the A&Rs or label the potential of the tune when it is finally released. There are a few exceptions - sometimes rough mixes have "character" and sound cool, or if the song is good/impressive enough they may offer to have someone in house clean it up for you (it's probably more common for them to ask you to clean parts up yourself though). Many labels also have in house engineers that do all of the mastering for their releases, and they'll take the mastering fee out of your paycheck. In general, I'd worry more about your mixdown than your master when sending a demo.
Other tips that might be helpful:
Always send a private soundcloud link, dont attach sound files to your email (if that wasnt obvious already). Keep your email text short and concise, they dont care about your entire life story. Careful if youre making your file downloadable (unless it is a promo) unless you know or trust the person you are sending your song to. In some cases, I've sent clips rather than full songs for consideration, and still receive either a response or an offer to release in the future.
TLDR - make a good song, get the mixdown sounding as good as possible, send a private soundcloud link, and wait a couple weeks or so. Most/many labels do not respond to demos they arent interested in, but generally it can take up to around two weeks for them to get to your sound unless they are really on top of things.