Yes, it's possible to install Ubuntu 12.04 on an EFI-based system. Yes, there are also potential problems. Secure Boot is one potential problem. Another is that some computers have broken EFI implementations that don't honor their NVRAM boot loader settings, meaning you must copy your boot loader file to
EFI/BOOT/bootx64.efi on the EFI System Partition (ESP). There are an assortment of other potential minor EFI-specific problems, most of which are fairly rare.
In a worst-case scenario, you should be able to install Ubuntu in BIOS/legacy mode -- most EFI motherboards support this type of operation. This may be limiting in the future, though, particularly if you've got an over-2TiB disk and you want to install Windows to it.
Overall, I'd say: Just try it. If you run into problems, look for help in the forums or check here. (There are lots of EFI-related questions here, along with answers to most of them.)