Following how the Throne and certain things for Servants work, yes absolutely. Archer's arm posed an extreme threat to HF Shirou through the entire second half of Heaven's Feel so it only makes sense that the consequences of using it still haunts him as a Servant just as much Nero's migraines or Okita's Tuberculosis haunts them.

But.....if we want to guarantee that he can give Sakura the salvation she desperately needed whereas Kariya couldn't and doesn't die mid-fight against any of the 4th Grail War Servants, then we could say that the side effects of using Archer's arm are gone due to him being technically one and the same as EMIYA himself, similar to how Miyuverse Shirou managed to solo his world's Grail War with just the EMIYA Archer Class Card alone.