Can I convert a Ubuntu 14.04.1 64-bit server to an ESXi 5.5 VM?

Are you trying to hot clone? If so, you need to use VMware vCenter Converter Standalone 4.0.1 I believe. First create an account at my.vmware.com, then search for "VMware vCenter Converter Standalone". On the "License & Download" tab at the bottom of all the 5.x downloads is 4.0.1.

I just tried what you're attempting. I found 4.0.1 to be the last supported version for Linux. I installed it on my Ubuntu 14.04 laptop (that also has VMware player). To run after installing, issue:

sudo /etc/init.d/vmware-converter start

I tried to do the P2V but got stuck on the "destination" section during conversion -- it kept asking me for credentials but didn't realize it was asking for an ESXi host somewhere else on the network to "accept" the VM. I never did succeed though because I don't have hardware support for an ESXi host, and also don't know if I could alternatively use VMware Player on my laptop to "accept" the VM.

I am not 100% positive on my answer I'm just giving feedback because I just did this last week. Or tried to anyway.

See diagram about hot cloning Linux on top of page 15 here, 4.0.1 User guide: http://www.vmware.com/pdf/converter_standalone_guide401.pdf