If I understood both approaches correctly, it should. (e.g. in your case you need to add the intercept and both sd parameters). Also note that the hypothesis function in brms makes a lot of those tasks simpler (it not only tests a hypothesis, but also returns the samples of the formula you wrote for the hypothesis). If you find the results differ, there is an issue (feel free to ask here if you see something weird there).
Oh, I think I understand (but I am honestly a bit out of my depth with this question, so please check my reasoning).
brms does not work with the concept of weight directly. It just assumes that the observed effect in each study is drawn from a normal distribution with mean mu (the linear predictor in brms, in your case the intercept + both the random effects) and standard deviation given by the se term. Now, according to Wikipedia for a simple meta-analysis (a single random effect) this seems to be equal to weighting the studies by their precision (inverse squared standard error) and running an appropriate correction. In the two-level structure you have, you could either claim that the weight stays the same, but the correction becomes more involved, or you could somehow try to correct the weight to make the original correction work… But I honestly don’t think any of this makes a lot of sense.
You could presumable make some sense of the total sd of each study around the global intercept (i.e. sqrt(sd_study ^ 2 + sd_substudy ^ 2).
One final note is that your model assumes the variation of substudies within each study is the same (e.g. two groups may have different mean effects they produce, but they will have the same sd of the effects). Which I am not sure is desirable - on the other hand, it would likely be hard to estimate a per-group SD so this is probably a sensible compromise.
Hope that makes at least a little sense.