Is it possible to have a cathode ray discharge in a non vaccumed tube while having a low pressure?
You could rephrase the question as: what problems will I encounter if I gradually increase the pressure?
A colleague of mine who used to design cathode ray tubes explained that the main reason for pursuing a high vacuum is lifetime. With some residual pressure, the tube would still work, but any (positive) ions that are formed due to gas-electron collisions will be be accelerated to the cathode - 20 kV potential difference - and then hit and damage the cathode.
If you don't care about lifetime, the CRT would still work for a while, but I'd guess that the next big issue at higher pressures is that you would form a big plasma discharge, like in a fluorescent tube. The power supply is not designed to handle that and will probably fail. According to Paschen's law, gas discharges may start occuring if the pressure is 10 Pa or so, depending on the voltage, gas type, and size.
Well, "low pressure" could be considered almost any CRT built by man, since it is very, very hard to achieve a true, absolute vacuum. Cathode rays were systematically observed in Crookes tubes at 10^-6 atm, which is definitely not a vacuum, but can also be considered "low pressure".