Should I take time to clean my circular saw blade after cutting pressure treated lumber? Since fasteners other than stainless steel or galvanized can corrode when used in pressure treated wood, is it going to cause my blade to corrode? Or is it only prolonged exposure?
You have to cut the wood somehow... You can give your blades a wipedown with a slightly damp rag to remove sawdust particles (let them air-dry well afterward), but I wouldn't worry too much.
Corrosion involving PT lumber is mostly a problem with long-term contact; the copper compounds in the chemical treatment are more "galvanically noble" than many common metals including carbon steel, and so an electrochemical reaction will result in the less noble metal (here the steel or iron) oxidizing. The same happens with ordinary zinc-coated or uncoated iron or steel fasteners in PT construction. To prevent this, stainless steel alloys (containing low carbon and higher concentrations of even nobler metals like chrome and nickel) or hot-dip galvanized fasteners (which cover the steel with a thick protective coating of zinc oxide which shields the fastener against further corrosion), are recommended for long-term contact with pressure-treated wood (on the scale of years).
However, your carbon-steel/carbide saw blade will only be in contact with the wood and its chemicals for some seconds. Your saw blades will dull naturally through age and use before the chemicals have any detectable effect.
I recommend the following procedure after cutting treated wood:
Cut several pieces of untreated wood. Clean the blade and surrounding with a cloth with little synthetic oil on it.
Repeat this procedure several times always using a clean fresh cloth.
Here's why I recommend this: It is difficult to reach every point of your saw blade when just cleaning it with a cloth or paper. Cutting wood makes the cut fibers go nearly everywhere. The can pry out even other particles which are clogged in small grooves on the surface of the blade.
So why use oil when wiping between the cleaning? The copper particles are somewhat soluble in water. And water is needed for the galvanic reaction between your blade and the copper particles. And once the corrosion reaction is started it tends to continue even if the primary cause is removed. So I think it is good to prevent any water from interacting with the copper compounds.
Of course, as @KeithS states, your blade may die from normal wear down before corroding away.