Yes because it’s reflective of a broad Z-circulation and a strengthened NPAC High, which directly teleconnects to enhanced Indo-West Pacific Convection (which requires a strong Walker Cell, and thus augmented equatorial trade winds). Simply put.
Although there are a slew of other methods to hypothetically reconstruct ENSO, I find lower frequency off-equator sub-proxies tend to offer the most insight and the best consistency.
I assume you mean quadratic, not parabolic (the latter can refer to both quadratic or exponential functions). And yes it just barely meets a quadratic fit if you actually run the data. The modest acceleration of the SLR post-WWII is a consequence of added anthropogenic/GHG forcing, while the pre-WWII warming/SLR is naturally/internally forced.
As for ENSO, reconstructions of the PDO (and SW US precipitation as well) are a good secondary proxy for low frequency ENSO tendency. Notice the previous prolonged -PDO era was during the Medieval Era, which also coincided with the last SW North American Megadrought and Cycle of General Climate Warming.