This is a question to hopefully untangle the sometimes confounded notions of statistical significance and effect size. As far as I understand, sample size intermediates the relationship between them, such that, while often low $p$-values will correspond to large effects, you can get significance for small effects with a large sample size, or vice-versa – an effect that you know is large may not reach significance because of an unsuitably small sample size.
Would it be correct to say that, given an independent samples t-test for a fixed sample size $N$ (2 groups of $N/2$ subjects each), the measure of statistical reliability ($p$) is really the same as (i.e. has a simple dependency on) the measure of effect size (e.g. Cohen's $d$)? In other words, if keeping $N$ constant, then significance ($p$-value) will be reached as soon as the effect size ($d$) exceeds a certain threshold?