Does converting rest mass to energy instantly change the gravitational attraction it exerts?

Before the fusion process gravity was acting on the systems mass plus the two hydrogen atoms. After it is acting on the system plus the helium. There is less mass and hence the gravitational Interact is less (negligible but still).

One subtle thing about gravity that only arises in situations like this is that the source of gravity is actually something called the stress energy tensor. This includes energy, momentum, pressure, and stress. So even though light does not have mass it still gravitates since it has energy and momentum and pressure.

This is important here because not only does the fusion produce helium, it also produces neutrinos and light. The sun doesn’t lose gravitation until the neutrinos and light actually leave the sun. For the neutrinos that happens quite quickly, but for the light it can take a long time as the light is repeatedly scattered, absorbed, and re-emitted.

There isn't actually less mass after the fusion reaction.

In relativity, the mass is defined by $$m^2 = E^2 - \mathbf{p}^2$$ where $E$ is the energy and $\mathbf p$ is the three-momentum. These should be taken as the sums over all particles in the system, and they are always conserved. Therefore, the mass is also always conserved.

Since the equation is non-linear, mass doesn't just add. While a single photon is massless, the system of a a hydrogen atom and a photon has more mass than just the hydrogen atom. Indeed, a gas of many photons can have mass, even though it's made up entirely of massless particles.