Yes there is shooting with .22s up to and beyond 200 yards.
BPCR .22 Metallic Silhouette is an extremely specialized sport that shoots out to 200 metres, but there are others.
http://www.22bpcra.org/history-objective.html
I think you should get proficient at 50 and 100 yards before you start at ranges that are really long for the caliber, though.