Will I have problems running 16' deck boards through a planer and will I get a nice result? Will the pressure treated chemicals, or the years of tree muck adhered to the surface of the boards wreck the planer blades?
In terms of chemicals, it depends. ACQ (Alkaline Copper Quartenary) treated lumber has high levels of copper, which can promote corrosion of steel (I think due to galvanic corrosion in the presence of water, which can act as an electrolyte). The older CCA (chromated copper arsenate) lumber does not have this problem.
There should be no issue running pressure-treated boards through a planer, however, if you do a little housekeeping afterward. Give the planer a good blasting off with an air hose after you finish for the day to reduce the amount of PT sawdust left in the machine. The ACQ chemical needs time (and water, I believe) to begin corroding the steel parts. One day of the sawdust sitting there shouldn't really hurt anything.
The years of tree muck might be a bigger issue. Hardened sap can dull planer blades pretty quickly, as will the years of accumulation of dirt and grime.
Another possible issue is stray metal pieces embedded in the decking that you would miss with a visual inspection. You can buy a metal-detecting wand to try to pick these out, but that's a tedious process for the hundreds of linear feet you'll be processing as compared to just buying new stock.
I'm trying to convince myself that purchasing a $500 thickness planer and planing 1/16" or 1/32" off the surface of the boards is a better use of funds than just buying new boards.
If you don't have a planer already and want one for the shop, now might be the time to get one if you can use it for this project as well. I would be prepared to buy a set of sacrificial blades if you plan on using it for the decking since there's a very good chance they will get trashed.
Consider also the time invested in processing the boards plus the cost of the planer vs. the cost of new boards. Your time is valuable, too.
As a final note, you might just try flipping the boards over to expose a "fresh" side. My uncle recently did this for his deck and it worked surprisingly well.
As always with all pressure-treated lumber, don't burn the waste. The chemicals are no good for your lungs to breathe in.