Yes it would.
Linoone is a Normal type which in normal conditions is immune to Ghost type moves.
A Ring Target when attached to a Pokémon, allows the Pokémon to receive damage from the opponent regardless of any type immunities.
So if you used Switcheroo on a Gengar who was holding a Ring Target, Gengar would be able to hit you with Shadow Ball and effectiveness would be 1x.
Source: Knowledge and Experience
Hope I helped :)