ESXi will work in a 1u form factor without problem from a technical standpoint if it is on the http://www.vmware.com/resources/compatibility/search.php , and you can purchase more public IPs or perform NATs, however, I might consider some alternative solutions for different reasons.
ESXi, without access to shared storage and vcenter is only useful as a partition mechanism.
You are going to increase the single-point-of-failure aspect of the solution - one physical failure could take out a large number of VMs.
There are alternative solutions that may be better for partitioning, depending on the operating system selections in question.
Virtual machines, depending on operating system, may be ram intensive, and 1u servers are generally significantly more ram limited than 2u servers, but you will have to compare that vs. the increased colocation costs of a 2u server.
VMware licensing for vram may mean your solution is inefficient
If you have customers, your SLA with them may have to reflect some of the downside of above.