From what I have seen in the literature, some researchers consider Modoki La Nina as a La Nina "flavor" and some do not. One reason for not distinguishing Modoki from canonical La Nina is that La Nina typically is centered more toward the central Pacific than El Nino under normal circumstances (see, for example, this post). There is more of a distinction between eastern Pacific and central Pacific ("Modoki") events for El Nino, as stronger El Nino tends to centered farther east than weaker events (see this post). 

With that said, it's conceivable that some La Ninas are centered farther east or west than others, and that could have an impact on the teleconnection patterns. Some have argued that the more central Pacific nature of the 2015/16 El Nino contributed to the drier than expected southern California. So, I wouldn't rule out that a more Modoki-like La Nina also could influence the western US precipitation, but I also know that subseasonal variability unrelated to ENSO often is a plausible culprit for unexpected weather patterns.