Are you existing hosts using dVSwitches or standard switches? If Standard, you could do the following:
1. Deploy new vCenter
2. Disconnect Host from inventory on VCSA 5.5
3. Connect disconnected hosts to VCSA 6.x
As a general rule, always remember that the vCenter must always be the same or higher than the version of the ESXi host.
So in this case he can do it safely.
If you want to try a vCenter upgrade instead, you can follow this guide:
Make a backup of the vCenter configurations before each update.