Can multiple sidekiq instances process the same queue
Nope, I've ran Sidekiqs in different machines with no issues.
Each of the Sidekiqs read from the same redis server, and redis is very robust in multi-threaded, and distributed scenarios.
In addition, if you look at the web interface for Sidekiq, it will show all the workers across all machines because all the workers are logged in the same redis server.
So no, no issues.