Trolley, it really depends on the amount of snow that year and how fast it is melting off. You really need to wait until sometime in March before knowing as some years get a lot of snow late. This year, you definitely wouldn’t have needed it. But in 2006, you would have definitely needed it.
However, an ice axe on the PCT is only used for self arresting. It is something easily practiced in an hour or 2 on a nice snow covered hill. I think there was a video on youtube showing you how to use one. Most thru-hikers on the PCT are in the same boat as you and they manage fine.
Miner