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 2.810^10 joules per year (or 3.110^-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 2^-40 kg per year if it was losing mass at a constant rate.