"Can you use their queues and database tools w/o using EC2?"
Yes, you very easily can. RDS is a simple setup, and so is SQS (queuing). The same goes for Dynamo and Redshift.
If you have a dozen slow (100us) switches, three slow (2ms) routers, and 500 kilometers of fibre (2ms), you should still be under 10ms each way. And that's enough gear to cross some countries.
I'm curious how you can do much worse than this in a data center. Maybe some pokey "application firewall" or massive buffer bloat?
At most it's been 4 to 6 ms. And that has coped with our heaviest load.