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 shouldcould 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 was a little concerned about how to interpret the deviation (-0.5/0.5) coding here, but I think because there are only two groups, it doesn't matter. Namely, according to https://stats.idre.ucla.edu/spss/faq/coding-systems-for-categorical-variables-in-regression-analysis-2/#DEVIATION%20EFFECT%20CODING, it says, "DEVIATION CODING: This coding system compares the mean of the dependent variable for a given level to the mean of the dependent variable for the other levels of the variable. In our example below, the first comparison compares level 1 (hispanics) to all 3 other groups, the second comparison compares level 2 (Asians) to the 3 other groups, and the third comparison compares level 3 (African Americans) to the 3 other groups." Since in this study, Sex is composed of only males and females, comparing "level 1" (e.g.) to "all other groups" would just be comparing males to females here.
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.