Will my certified system work with the latest Ubuntu Release?

The short answer is 'probably', if the system has been certified with Ubuntu at some point then unless a new bug is introduced into the kernel affecting that systems hardware, then it should continue to work. The likelihood of that happening increases depending on how many release ago the system was certified compared to the one you want to use - so if the system was certified with 12.04 LTS and you want to use it with 16.04 LTS then there it's more likely something will have broken then if you use it with 14.04 LTS. However even that is subject to a lot of ifs and buts.

You can download Ubuntu and prepare a boot USB stick, then boot your system with this USB and select "try Ubuntu without installing", this should give you a good idea of the level of support for your system. If you're satisfied with it, you can proceed to install and use Ubuntu as normal.

http://www.ubuntu.com/download/desktop/create-a-usb-stick-on-ubuntu

Note about Servers:
The above should also work for Ubuntu Server ISOs, however, Ubuntu Server ISOs do NOT have the "live" environment that the Desktop ISO does. Your best bet would be to try the Live Environment with the Desktop image as described above, and then deploy the system using the Server ISO.

If you are considering upgrading, then in most cases, the upgrade should work. However, as with anything, upgrades can break and can cause loss of your system. Before undertaking an upgrade from one version to the next, you should ALWAYS back your data up and never blindly upgrade on a mission critical system.