People who say you can't raid at 350ms are just making assumptions since clearly they themselves have never experienced it. As one of the people who has raided at that latency, along with others in this thread who have also raided at a high level with that latency, I can say that you definitely can raid effectively at 350ms. Look into a tunneling service like lowerping, smoothping, battleping or reducethelag though, it should help you.
There are two arguments here in this thread so far,
1) Will it affect the dps- If you are playing a spec with any sort of resource downtime , the effect of latency on your dps is minimal or close to zero , so you are safe if you are playing any of the melee classes . but if you are a caster , even with spell queuing you will loose bit more dps, as their motto is ABC (Always be casting). You can even check it for yourself by simming the theoretical dps in simcraft by setting the latency to low (<150m) and then to medium (150-300ms) and you will see
2) Will it affect the reaction time to boss abilities. There are few abilities that require sub 1 sec precision , with most being safe if you react within 1sec or in your case 1-0.7(.350x2) = 0.3sec, you have to be real attentive and focused and react fast with your lag there will be no breathing space. I had been on cloak-soak duty on ultraxion hc as rogue and with 200ms I was able to do it flawlessly. Other stuff like ground fire effects , which you think you have moved out of and server will disagree, again will happen rarely if you are really fast at reacting.
TLDR- Absolutely playable at 350 ms competitive , bit of a dps loss as casters , and have to have fast reaction times.