How far-reaching is the effect of conjugation?
1,6-additions are indeed possible (1) but since you have competing 1,4-addition and 1,2-addition it becomes more difficult. To push it to the 1,6-addition bulky organometallic catalysts are used. Reaction pathways are also determined by the electrostatic interactions, and these diminish the further away you get from the carbonyl.

(1) https://onlinelibrary.wiley.com/doi/epdf/10.1002/adsc.201601342, https://www.organic-chemistry.org/abstracts/lit1/353.shtm