Not a definitive answer, but I note the following.
The solar photospheric abundance of Thorium is indistinguishable from the abundances in the protosolar nebula deduced from meteorites (to within 0.1 dex, Asplund et al. 2009). Of course it might be thought possible that Th-depleted material in the centre of the Sun never makes it to the photosphere. However, this is not the case for other elements such as Li, which really are depleted in the solar interior and this is reflected in the solar photospheric Li abundance. So there are deep mixing processes at work, extending well into the solar radiative core (and whatever they are, they happen during the main sequence lifetime of the Sun, since pre-main sequence Li depletion is almost non-existent in solar mass stars - e.g. Jeffries 2014), that would be capable of bringing any Th-depleted material to the surface. Asplund et al. also comment that it is thought that radiative diffusion only reduces the photospheric abundance of heavy elements by a few hundredth of a dex. I would conclude therefore that Th survives intact in the solar interior.
I have not been able to find a reliable source for the photospheric Uranium abundance - the abundance in meteorites is very low and so the lack of good measurable lines is consistent with this. Grevesse (1969) outline the problems and derive an upper limit considerably larger than the meteoritic abundance.
Thus, from an empirical point of view, there is reasonable evidence that Thorium survives on 4.5 Gyr timescales inside the Sun.
Why would this be? The pp-chain does result in gamma rays with energies of a few to tens of MeV. But the reaction rate is not that high and the abundance of very heavy elements in the Sun is very low. It is overwhelmingly more likely for the gamma rays to interact with electrons and protons first. Maybe Chris White has this calculation in mind? The other issue to explore is whether photodisintegration/photofission is actually likely with $\sim 10$ MeV photons. This paper suggests it is possible, as does the paper by Findlay et al. (1986) who measure the cross-section of Th to photofission at about 6.5 MeV.