I am making a cake topper using wire. I want to attach 3 hearts in a row on each wire. I really don't want to try to thread them through the wire. Can I attach them using royal icing having 2 hearts back to back? Or is there a better way? Any help would be great!

Yes you can do as you explained. OR you can use gum glue to stick them together. OR use fresh fondant &/or gp. You can glue wet to wet or wet to dry fondant or gp but no way to make dry to dry stick w/o adding some fresh/wet between them.
Don't know of a better way except to thread them.

Thanks for the help.