The scenario where Jupiter just drops into the Sun from its current position would certainly have short-term effects. NB I have not yet considered an alternate scenario where Jupiter is drawn closer and loses its energy and angular momentum gradually as it gets nearer and nearer to the Sun.
The kinetic energy of Jupiter at the Sun's surface would be of order $GM_{\odot}M_{\rm Jup}/R_{\odot} \sim 10^{39}$ Joules.
The solar luminosity is $3.83 \times 10^{26}$ J/s.
The addition of this much energy (if it is allowed to thermalise) would potentially affect the luminosity of the Sun for timescales of tens of thousands of years.
However, I suspect what is more likely is that the kinetic energy would be also be used to do work and lift the convective envelope of the Sun. In other words, the Sun would both increase in luminosity and in radius. If the effects were just limited to the convective envelope (it is unclear whether the plummeting planet could survive falling to even greater depths), then this has a mass of around $0.02 M_{\odot}$ and so could be "lifted" by $\sim 10^{39} R_{\odot}^2/GM_{\odot}M_{\rm conv} \sim 0.1 R_{\odot}$
So in this scenario, the Sun would both expand and become more luminous. The relevant timescale is the Kelvin-Helmholtz timescale of the convective envelope, which is of order $GM_{\odot}M_{\rm conv}/R_{\odot} L_{\odot} \sim $few $10^{5}$ years.
On longer timescales the Sun would settle back down to the main sequence, with a radius and luminosity only slightly bigger than it was before.
This all assumes that Jupiter can remain intact as it falls. It certainly wouldn't "evaporate" in this direct infall scenario, but would it get tidally shredded before it can disappear below the surface? The Roche limit is of order $R_{\odot} (\rho_{\odot}/\rho_{\rm Jup})^{1/3}$. But the average densities of the Sun and Jupiter are almost identical. So it seems likely that Jupiter would be starting to be tidally ripped apart, but as it is travelling towards the Sun at a few hundred km/s at this point, tidal breakup could not be achieved before it had disappeared below the surface.
So my conclusion is that dropping Jupiter into the Sun in this scenario would be like dropping a depth charge, with a lag of order $10^{5}$ years before the full effects became apparent.