Yeah, but it does have 10^67 years to catch it.

Assuming the light isn't bending at all, I think it should get about 890 watts of light, or 2.8x10^10 joules per year (or 3.1x10^-7 kg per year?) from the sun, which should be enough to cause it to grow, at least while the sun is still around. I expect it would get a lot more mass from gasses, meteors, and dust in that time frame. Based on your numbers above I think it should only be losing like 2x10^-40 kg per year if it was losing mass at a constant rate.

There's only about 50 watts per square meter out that far from the sun! We get about 1300 here on Earth. Jupiter's orbit is a lot larger compared to Earth's than people normally think.