I wouldn't run it in the reactor merely due to the extremely small pellet size. Even the canister filter on my planted tank is able to force some of the pellets through the fine mesh bag whenever I clean the filter and recharge the purigen.
I also wouldn't worry too much about it completely stripping nutrients to the point that the corals suffer. I've used purigen on my planted tanks for years, and can honestly say that I've never noticed a decrease in available nutrients as a result of either adding purigen to the system or recharging the media...and this was in a tank that was getting daily doses of nitrate, phosphate, potassium, and micronutrients. I tested daily for nitrate and phosphate, and weekly for iron and copper while figuring out the dosing regimen over a few months. The purigen did effectively polish the water and removed tannins, but had no effect on nutrients.
I'm also running Purigen on my 28 gallong JBJ nano right now, and just have the bag sitting in the middle chamber of the media basket. I started running it after adding some coral to the tank, and didn't notice any stress or bleaching. FWIW, I did notice my hammer shedding off some zooxanthellae after adding a skimmer to the tank whereas it was unaffected by the addition of purigen.
I know most of my experience isn't with a reef...but IME nutrient availability shouldn't be a huge issue.
edit: To add to my post, answers to previous inquiries directed toward Seachem about the product's use in planted tanks and the potential for detrimental nitrate reduction pointed out that purigen removes the organic waste prior to conversion to nitrate. In other words, it interrupts the ammonia - nitrite - nitrate cycle by removing waste before it's ever converted to nitrate. I am running a fairly large amount of Purigen in a heavily stocked planted tank and still have 5-10ppm of nitrates in there without dosing KNO3...the purigen likely removes some of the organic waste prior to conversion...but definitely not all of it.
Hope that helps...