Blukote is an antiseptic for wounds.I thought it was fine because people put blukote on feet so chickens leave other feet alone, so if you put some blukote on the egg, then maybe they will leave it alone.
The blue color is supposed to camoflague the red blood to keep other birds from pecking at it(which often doesn't really work and can actually attract pecking).
So, no, I seriously doubt it would deter egg eating.
I'll repeat:
How often?
Are the eggs they eat hard or soft/weak shelled?
Figure out why/when they are eating eggs then we can come up with a solution.