As the direct anwer to your question is ‘absolutely no’, I will try to build up some ways leading to the skies you wanted, but there will be some points where persons with a deeper insight into physics then I have will have to fill up my ideas with hard facts.
First option: the mars-like dusty skies This is definitely the easier way and scientifically feasible. If your planet has a high part of dust or other ‘pollution’ in the air, you could get a reddish sky as we can see it on mars or even sometimes on earth if the sun has the right angle (sunrise and dawn). You just have to care about how this dust influences
Second option: high-atmosphere glowing neon
This idea is a bit special and I don’t really know if it could work in reality. Your neon itself wouldn’t give you a sky coloured in any different colour as it is a colourless noble gas. Furthermore as a noble gas with an atomic weight of 0,9g/l it’s a bit lighter than air and not chemically bound so it would mainly rise up in the higher layers of the atmosphere and would get lost into space (as probably happened to our earth). So at first you would need a layer of any kind (like our ozone-layer but I don’t have a good idea at the moment and ozone is not sufficient) able to hold it in a high atmosphere layer. Second you need a star with a high radiance which is able to penetrate this ‘prison-layer’ without destroying it and get the neon (which should be highly concentrated in its layer) stimulated to higher energy levels. The discharging neon would give you a permanent orange/red glow in the higher atmosphere which could get you to the skies you wanted.
Third option: bromine You could get a reddish sky by adding a high level of bromine into your atmosphere as it is a red/brown gas by itself. But as bromine is toxic to earthly plants and animals this will be the option with the most difficult afterwork as it would lead to a totally different evolution, changing nearly everything.