I've been talking to my FIL about getting into archery and he has been very helpful and supportive.

He told me that instead of getting a brand spanking new bow, I should consider a used bow (he said he'd help me look them over before I'd buy it) because the value drops off after the next model comes out for a particular line. He said his Anarchy would go for a couple hundred less than when he bought it new.

Do bows really depreciate quickly? If so, why? If it still has the legal draw weight and can accept all the current addons/technology why would it be cheaper?

They go down fast just like computer tech because pretty much every year they get that much better.  Or at least the marketing side of it is that good.
For example, I had a Hoyt Maxxis 31 brand new in 2010 set at 58 pounds.  I bought a new Hoyt Carbon Element 2012 at 65 pound draw.  It was 40+ fps faster, quieter, better accuracy and the draw weight felt easier at 65 than the 58 a few years earlier.

Makes sense. It sounded gimmicky to me, but I guess a few more FPS is worth it to some

I know a guy that buys a new bow every season and after one year of competing with it, he takes about a $150-$200 hit.  However, it allows him to sell the old one and fund a new one for very little.  I've always bought my bows 1-2 years old, then take them into a local shop for tuning and fitting for me.  I spend about $50 for the tuning and probably pay about 1/2 the price of the bow if it were new.