When I put Shedinja onto my bench using Ninjask's "Cast-off Shell" Ability, can Eviolite help protect it from damage?
No, because Shedinja is not a "Basic Pokemon"; it is an unevolved Stage-1 Pokemon.
Source: TPCi Rules Team (2012-08-23)

Relevant cards

Note: All applicable cards may not be listed below.
DP6_67
BW3_91
BW8_122