You can install and use PlayOn Digital Media Server or other software alike and this will allow you to watch netflix without connecting to the PSN but it wont be through the native Netflix app it will be through the media server and I believe it only shows stuff you have in queue, you can't search for movies or shows through the media server you have to add them from the Netflix website.
Using the native Netflix app and not requiring to sign into the PSN I highly doubt it at this point in the game. As far as relying on updates though like the recent 2.02 update allot of people were having issues with black screen and error codes so you can just edit the PARAM.SFO and change the version so the Netflix app doesn't check for for the 2.02 update...using this in conjunction with F**KPSN v0.5 obviously to access the PSN which is the most important, will allow you to watch netflix normally and is how I've been watching it.
Incase you decide to go with the second option here's a
You must login or register to view this content. with the Netflix 2.00 pkg and an edited param.sfo to bypass the netflix update.