Not quite. Gen 2's breeding makes it so that Pokemon always inherit IVs from the opposite gender parent only. This means that your shiny Pikachu's IVs will only be inherited by female offspring, which for Eevee, cannot be shiny.
However! The IVs that the female Eevee offspring will inherit is still usable as a "shiny gene." So if you breed your shiny male Pikachu with a female Eevee, all female offspring from that pairing will be non-shiny, but with dormant "shiny gene" IVs. This can then be passed down to the next generation for the 1/64 chance of hatching a shiny Eevee.