Yes, it should be possible, I did this on a Toshiba S855. Left secure boot enabled, and changed the boot order to boot usb first. I'd suggest pre-partitioning using a gpt partition table, make a 300M FAT32 bootable partition for EFI, and your favorite partition scheme for the rest. You must install from the "try" desktop however, because regardless of where you specify putting the bootloader, your hard disk's EFI partition will be the one mounted and used. To correct this wrong behavior, before starting the install have a terminal running, and have command lines you can recall (just for speed) which unmount the hard disks's EFI, and mount the target's EFI. Start the install, immediately after specifying the partitions, check in the terminal, do the umount/mount, and let the install proceed.The the Ubuntu files will be put onto the target. One big problem you avoid doing this is trying to boot Windows through grub -- Windows may not be seen, wrong grub commands will be used, and you need to run boot-repair just to fix all that up.
Removable media use the bootloader in /EFI/Boot/bootx64.efi (for x64 architecture), so copy
/EFI/ubuntu/shimx64.efi to /EFI/Boot/bootx64.efi (for secure boot, no need to turn it off). Also put a (signed) copy of grubx64.efi into /EFI/Boot/grubx64.efi. Have a copy of grub.cfg in /EFI/ubuntu/grub.cfg, and things should work. I think installs later than 12.04 will use a grub.cfg which pulls in the maintained copy in /boot/grub, but a full grub.cfg file works too -- you would need to update it when kernels get updated.
You probably want to take the execute permission off the /etc/grub.d/30_os-prober, since it won't see windows, and kills the timeout on the grub menu when it adds it's stub code to grub.cfg. I'd also suggest backing up the EFI partition files.