Personally, given the sizable cost of the tier pieces and the other great upgrades (compared to the aforementioned small upgrade of the sigil) I won't be getting it for months either. Ha.
I think it may stack up relatively quickly, definitely for DPS, and maybe a little slower for tanks. Off the top of my head, with Chill of the Thrown I'm sitting around 45% avoidance with raid buffs? Several of the bosses so far have nice quick attacks so without having a log to parse I think I've been getting about 50-60% melee-to-RS turnover, so it would take roughly 20-30 seconds to get the full stack, and a little less to approximate or pass the value you get from the previous sigil on a chance proc.