Thomas Covenant lived in America, but could have been of any descent. I prefer to think if him as being of European descent, but I think his swear-words are misleading.
If you take them at bloody face value, he does sound of English descent, but I contend that this was merely SRD's attempt to make TC foul-mouthed without actually using foul language. You might be thinking,
well, excrement of a pig! Why would he do something like that?
A) To remove one potential barrier to getting printed at the time he was writing, by not using 'flagged' words.
B) To use interesting wording that SRD invests with meaning to the reader, rather than relying on words that are so overused (f**k, s**t,) that they lose their impact.
Personal Sidebar [My mother is one of the calmest and nicest people on the planet, and when she swears, its like the Seventh Seal has just opened---because she so rarely swears, when she does you know she MEANS it.]
SRD switch-hits, though, doesn't he? As I recall, I think "Sheepf**ker" was one of Nick Succorso's occasional pet-names for Angus Thermopyle. But the setting of the Gap Cycle was so gritty/nasty that anything less would have seemed...silly. "Sheepravisher?" I think this was done intentionally to fit the hardened sci-fi tone, just as the fantasy realms (The Land and Orison) had softer language to fit their more lyrical tones.
So,
Bloody Hell and Damnation! I don't think his curse-habits should have a bearing on placing TC ethnically.
To answer the original question: I think TC is Swedish. Try reading his lines as if he were the Swedish Chef from the muppet show. "I'm not yer bloody Berek. Bork! Bork! Bork!"
DukkhaWaynhim