You can see the feature comparison here:
Compare VMware vSphere Editions: Managed Virtualization & Cloud Computing
In it, you can see the "Storage API" requires Enterprise edition. But I don't believe that's what you're referring to. I'm running several "Standard" edition vSphere licenses with Backup Exec and performing VM level backups. If you read the section on Storage API:
http://www.vmware.com/au/products/datacenter-virtualization/vsphere/storage-api.html#protection
I'm sure all you're interested in is the bottom section, which states "The vSphere API for Data Protection is included with all VMware vSphere editions and kits". So yes, essentials would be fine.
I'm not sure what you mean by "the very basic", either you are running the "free" edition", or the first licensed edition is "Standard", which includes vSphere API for Data Protection. A license upgrade certainly doesn't take a reinstall but if you don't currently have vCenter you will need to build a server for that vCenter.