Yep. Rubber oxidizes. Exposure to air causes oxygen molecules to attach onto
the long chains of the rubber molecules and over time makes them less elastic. A simple example is a rubber band that has been sitting in a box for several years; they become brittle and when you try to stretch them, the don't stretch but instead the rubber ruptures, tears and breaks because it did not stretch.
Another example is if you have ever seen a rubber that is 20-30 years old. It will be hard, brittle, not grippy and pretty awful if you tried to play with it.
And, not too different from what Lazer said, if you can't tell, it says more about you than about the process of oxidation and rubber deterioration.
That being said, if you can use the rubber and you can't tell the difference, that is fine for you. But for sure, Lazer is correct that, if you want the rubber to perform at its best when you use it, you should wait to open it until you are going to actually use it. Will you be able to tell if you open it now, try it, put it on the shelf for 9 months, and then start to use it? You may be able to tell and you may not. Based on your comment about the rubber left in your drawer for YEARS, you may not know the difference. But that does not mean there won't be one.
So, if you want to use it when it is giving you its best performance, either open it now and use it till you wear it out, or leave it in the packaging until you are going to use it.
You can do what you want. But the answer to your question is exactly what Lazer told you. So feel free to ignore it. But it makes me wonder why you ask all these questions where it seems that you don't want the actual answer.