They do but how much is tough to know
1) they add weight to the overall shoe. 1-1 an orthotic sockliner weighs more than a standard sockliner. Some can add 2-3 ounces to a shoe which is 50-80 grams. 100 grams weight saving translates approximately to 1% running economy. Easy to see the correlation here
2) They won't do anything to the plate (which has a minimal effect anyway) but they will alter your peak force through the shoe to the ground which is the most important thing in determining how fast you run (it's actually the only thing). New foams are so effective because they are easily compressible and do so fast. Simplistically this means you can optimize how much force you transfer to the ground which in turn gives it back to your mass and propels you forwards. Orthotics are denser materials that compress slowly and dissipate force - both counter to the peak force transfer scenario we are after. How much this is I have no idea. I think you could hypothesize its net impact is also somewhere between 0.5 and 1% though full disclosure this is just a guess.
So maybe in total you might see a 1-2% reduction in benefit using the clunkiest orthotics if that's what you needed to use. I guess that's somewhat significant but again, just an educated guess.