I think this is essentially the answer I was looking for: In Barr (2008): *Analyzing ‘visual world’ eyetracking data using multilevel logistic regression*, it is stated: "With **orthogonal polynomials**, the interpretation of each term in the equation is **independent** of all other terms (i.e., **inclusion of a higher-order term does not change its interpretation**). Thus, the **intercept term gives the mean height of the curve over the entire analysis window**..."

So, according to Barr (2008), it seems the estimate and *p*-value associated with the `Sex_c_centered` term should independently compare the mean outcome of the two sexes over the entire time-course (despite the other terms in the model). In light of this, it seems the associated *p*-value *should* indeed be a test of whether or not these two groups are different *on average* with respect to the outcome (which, here, is proportions that have been transformed with the empirical logit transformation (this is what `Elog` means on the *y*-axis of the plot)).

I am leaving this here as a tentative answer in case it is helpful, but am still open for feedback if something about this seems amiss.