Does Henry's law depend on curvature of gas/liquid interface?
No, but not because the vapour pressure of mixtures doesn't depend on curvature (it does), but because Henry is a narrowly-defined law that doesn't contemplate surface curvature.

Henry's law is, after all, a barely better description of vapour pressure in mixtures than Raoult, and that's because it introduces an experimental value (the Henry constant) for each solute/solvent pair. The only reason why it's (rarely) used is that it's extremely easy to operate with. And pretty much the only reason why it's taught is because it's a simple, mathematically trivial treatment that moves away from ideality; it's sort of the minimum, simplest step away from ideality, which is convenient for a classroom.

But if you attempt to combine Henry with the effect of surface curvature, say by combining it with Kelvin's equation, you run into a serious problem. The equilibrium difference of pressure between a liquid, $p^L$, and its vapour, $p^V$, when the liquid has a curvature of radius $r$ is

$$ p^L = p^V + 2\sigma/r$$

where $\sigma$ is the surface tension of the liquid. And that's when you run into a problem - surface tension of a liquid mixture also depends on the composition, so the entire point of Henry's law (that concentration of a species in solution is proportional to its partial pressure with a proportionality constant $H^{cp}$) is lost. Even if you accept the simplest case (that surface tension behaves ideally with composition following Gibb's isotherm) you are stuck with a $H^{cp}$ that is itself a function of $c$, and so the mathematical model has definitely moved away from Henry.

By which point you are better off using other, more realistic models for your non-ideal mixture. Note that even then, you are stuck with iteratively computing the crossed effects of surface tension on vapour pressure and vice versa, as the relationship can't be solved analytically as far as I know.