Nope not unless you want to keep playing the game for maybe 2-3 pyromancy spells in the painted world

To get to the Painted World, you need the Peculiar Doll from the Asylum and then interact with the huge painting in Anor Londo.

You get a pyro spell from upgrading Chaos Servant Covenant to lvl 2I believe

What if you visit the egg man while invading another player's world? Would you be able to interact with him as needed?