Does the degradation of the flat tappets affect emissions?

[Rough Edge racing]

Zinc and moly have different properties. The moly doesn't work as well. The problem with the wear is on initial break in. Once the initial damage is done the parts quickly fail.
Yes, there are oils with more zinc than others but the EPA limits the amount and it is lower than oils of the past. When the nre oils came out engine builders were using the new oils and suffering engine failure on the dyno. Inspection showed lubrication failure.
Go to your Chevy dealer and buy an engine. It will come with a container of break in additive. The stuff is heavy in zinc.
Race engine shops use the stuff. Once the break in is complete use your favorite oil.

 The limitation on ZDDP is for oils intended for use with catalytic converter vehicles. It's the oil with the "Starburst" on the label. There are many non Starburst oils still available with as much zinc as 20 years ago. Best place to get info from the the material data info on the oil manufacturer websites.
  And some engine do require  higher amounts of ZDDP after break in....OHV engines with aggressive cam profiles and many 1960's  British motorcycles...
  However, and the airplane guys here can correct me if I'm wrong...Light aircraft piston engines have flat tappets and aviation oil does not have ZDDP because of forming deposits....I don't believe cam wear is a problem because of the materials used to make the lifters and cams...

[Gootsz]

Well. Once those bits  start floating around and chewing up the insides and it starts smoking or seizes. Yea the emissions will go up.

micky

[Rough Edge racing]

 I had a high performance Chevy engine chew up a few cam lobes......The engine had about 500 miles on it so I disassembled it completely. Lobe debris, like grinding dust, was embedded in all the bearings and the oil pump. The high quality Wix filter did not capture all of it...I cleaned the bare block and components ,replaced the bearings and cam, quick hone of the cylinders and new rings...
 If you have a cam failure and debris, fine or coarse, gets into the oiling system....I would consider a complete engine disassembly and cleaning to be mandatory if you care about the engine. Yes, some just replace the cam and lifters...