Storing spare tube under saddle bag
I'll sum up some of the comments with some concerns that you need to address:


Excessive moisture
Temperature changes
Abrasion and movement
Access


Simply wrapping the tube in something non/semi-porous and opaque will help keep it safe from the elements, but not from temperature changes, but it sounds like that's not going to be too much of a factor. You should also consider any bits of dirt, water, road, mud that are going to be kicked up from your rear wheel under the saddle bag. This could cause some excessive wear after you installed the tube in the tire unless you clean it first.

As a few of the other comments have stated, you may want to consider other means of storing your ride supplies. You've got a spare tube but do you have a pump? Is it a frame pump or small enough to store in a bag? Tire levers and a multitool are also going to take up space. I'd recommend looking at either a larger bag or purchasing something like a hydration pack (CamelBak, Dakine, Osprey, etc.) to store your tools, clothes, food, and whatever else. That way you can plan a variety of rides without needing to awkwardly stow tubes, pumps, and anything else on your bike!

EDIT: (Kudos to Chris H) If you've already got a way of storing all that,you want to make sure it is secure and protected from dirt. It doesn't need to be sealed completely, as you want to make sure any moisture such as condensation can evaporate.