It should unless it is a seedling and not a known variety. I don't know much about growing citrus -- not many grow in south-est, central-est Wisconsin, but many citrus have thorns. I had an orange, lemon, and grapefruit tree. All of them had thorns; all were killed off before they had a chance to produce fruit or stab me to severely.
I don't have the slightest clue as of how to grow citrus (even though I think that kumquats may be possible in my area) but I can tell you this -
Many of the citrus fruits (excluding grapefruit) that you buy at the store are injected with artificial sweeteners just to make them as sweet as they can possibly be; the consumers want their citrus to be very sweet, so the big citrus growers make sure that their citrus are going to be what the consumers want them to be - very sweet. I am not sure if this is still going on (my guess is yes, it is) I just figured that I'd warn you that your tangerines may not taste as you may have expected they would. [They would also be homegrown and fresh from the tree (or bush?)]
Hopefully we'll get somebody that has some real experience with citrus on this thread.