It all depends upon what you mean by 'necessary'? Your requirements are your own. No one else can really address these issues. I would certainly recommend using oyxgen traps. I would also check your EPC and other pneumatics for any possible leaks of air into your carrier gas system.
These phases are proprietary to Restek, in other words, no one outside Restek is supposed to know that they are. That means no one can really forcast how well they will tolerate oxygen, or water, or alcohols. Some phases resist oxidation better than others.
Antedotal information may not be of real value here.
I have used their Rtx-Wax and Rtx-1301 for headspace analysis continuously (with oxygen traps and using high purity helium) with my previous employer and found them to be consistent and reliable for six months periods before I replaced the Wax column. The 1301 lasted a year which I think is reasonable for an analysis of residual solvents. (disclaimer: I work for a competitor of Restek) I found other suppliers columns to last equally well.
This was with heavy use injecting pharmaceutical headspace analyzing for residual solvents. (lots of sample air was injected)
best wishes,
Rod