According to my sources-
With an external database, the vCenter Server 5.x can support up to 10,000 powered on Virtual Machines and/or 15,000 registered virtual machines (http://www.vmware.com/pdf/vsphere5/r55/vsphere-55-configuration-maximums.pdf). Its not necessarily what we can support, but rather what the backup application can handle. That said, we only support ~100-180 concurrent connections to the vCenter Server depending on the API choice - see page 7 from the maximum guide - so that could limit the number of connections to the vCenter Server in one swing (and not to mention their backup vendor better have a good cleanup mechanism or it'll lock up the vCenter Server if they try to push the limit).
So, long story short, they need to be engaging with their backup vendor on those numbers in terms of number of connections that can be perf ormed by the backup 'appliance' as well as the number of VMs that can be done in one connection/session; some backup vendors allow for multiple appliances to be deployed to allow for more backups to be performed at one time.