I understand that the O.G. of wort increases after the boil if the water that evaporates is not replenished. However, what about the hops added during the boil? Do they bump up the reading on the hydrometer? If so, how can we compensate for this in our calculations?

Provided you have no hop debris in you hydrometer sample test jar/tube keeping the hydrometer from floating freely then the hops should not bump up the reading.

Hops won't affect gravity.

Consider a 12 °P beer. It has specific gravity of about 1.048 so each liter weighs 1046.12 grams and contains 125.534 grams of extract. If you bitter this beer to the extent of 40 IBU you will have added approximately 40 mg iso alpha acid. Assume 60 mg of other stuff dissolves as well. The hopped beer will now contian 125.634 grams of extract which corresponds to about 125.634/1046.22 = 12.0084 °P. As °P and SG are nearly linearly related by 1 °P ~ 0.004 SG this change of 0.0084 °P implies a change in specfic gravity of 0.000034. This would be detectable with a good U-tube densitometer but for all practical purposes you can assume that the hops do not increase extract.

This reminds me of the time I attempted a gravity reading of raspberry puree. Knew pretty quickly it wasn't gonna work, sure enough, the hydrometer didn't sink at all.

Nice! But I'm sure it was still fun!

Love how AJ chimes in to set us all straight! Thanks for the real truth!