Hello,
my advice is not to install it (don't understand me wrong) 
. it's the advice that you should think about it.
what do you mean with " you don't need new vCenter" ? It's not a new ones. it's having Upgrade Process integrated.
So for my own Taste > i wouldn't use an such old Build Number anymore. Once theire are a new ones out i wait some weeks - and if no hard Problems are known i push it for usage.
i'am confused. why you like to use the "Appliance Upgrade" ? you don't have a Appliance as i see. you have a normal Windows Machine where you installed vCenter. (just download the normal Iso for the vcenter).
VMware-VIMSetup-all-5.1.0-880471.iso
if you never didn't upgraded a vCenter > i would suggest that you make a Backup before doing that.
So if i would be you i would make following at first Step now:
- check SSL Cert.
Best regards
max