First of all, your worker processes should be running. Check this:
ps = Sidekiq::ProcessSet.new
ps.size # => 2
ps.each do |process|
p process['busy'] # => 3
p process['hostname'] # => 'myhost.local'
p process['pid'] # => 16131
end
ps.each(&:quiet!) # equivalent to the USR1 signal
ps.each(&:stop!) # equivalent to the TERM signal
From https://github.com/mperham/sidekiq/wiki/API#processes
So if they do - you can enqueue more work. The only case when tasks can remain in the queue while your worker processes are working is when the worker processes are processing jobs slower than they come in. Then your queue will grow and newly enqueued tasks will not be processed until all previous jobs are done. But this is your responsibility to figure out why your workers performing slowly.
Hope that helps!