It might, locally (so El Paso). However, it's an old fault, the period on it is pretty long (time between significant events), and it's cut off from major driving tectonics (meaning when events happen there it's because of compression from other places further away vs it being on an active crustal disturbance (vent). so the impact is normally lessened). Think of it like being the 18th or 19th car in a 20 car pileup. Yes, you may take a nasty bump, but you're likely driving away from it vs the cars at the back end because most of the energy has been absorbed by the cars between.
Never say never. Faulting and plate tectonics are not a precisely understood science and even a small fault can throw a major snap. But your odds are pretty low.