I wouldn't.
Because of the 2" top opening, you can't get in to clean it properly, to aerate the wort, and to dry hop if you go that way, amongst other reasons,.
Good for keeping your beer in rather than using bottles, or possibly for conditioning, but not for a primary fermentation.
Not sure why you need a sugar thermometer. For homebrewing you need something that will measure temperatures reasonably accurately in the range 0-100*C. I use a cheap digital thermometer from ebay about ã2.50 which works fine for me. Others use more sophisticated thermometers which cost more but do the same job.