Yes. You just need to format the SD card using the FAT32 file system.
The SDHC specification originally supported up to 2 TB, but this was later reduced to 32 GB because it turns out that FAT32 has rather awful performance and disk usage compromises above 32 GB. exFAT, which is part of the SDXC specification, solves most of those issues at the cost of compatibility and patent licensing.
Like @GerbilSoft said, yes, it's totally possible. I had a 128GB card in my old Wii at one point, before moving my GameCube games over to the USB hard disk I have plugged into the console. You just need to format the card using FAT32, with a 32 kilobyte cluster size (which should be the default cluster size for FAT32).