Q: Is it sensible to write $\bar{\bar{\alpha_1}}$? Continuing this, could you write: $\bar{\bar{\bar{\bar{\alpha_1}}}}$?
At what point do such characters become obtrusive?
Just curious. What other notations could you use, similar to this?

A: There are no hard and fast rules on what notation is allowed.  Some forms are pretty much standard and agreed by (almost) everyone.  Some are common but not universal.  Some are quirky and individual.  You can use almost anything that you like as long as you define what you mean by it. You might want to pay attention to the readability and whether or not something nicer may be possible.  
There is no central mathematical committee defining what is and is not allowed.  
