You could and be easily understood. A more common way to say it focuses on the friendship rather than the friend: "a friendship that has stood the test of time."

It would be understood. Probably an easier way to say that would be like above "A friendship that has stood the test of time.". "A lifelong friend" would also be something you could use.

time is the best invigilator the world has ever witnessed. And it invigilates friends. What type of catastrophic crisis and who comes to rescue, time decides.

It's perfectly understandable, but you need a hyphen: a time-proven friend

It's a nice phrase, and a poetic one, too. Even though it isn't standard English, we would understand what is meant by it.