No, not really. At least, every dictionary I’ve ever consulted indicates that the etymology is uncertain, and sometimes also that any link to the Welsh people is dubious. If @engineer_comp_geek has uncovered evidence firmly establishing the word’s origin, I can introduce them to some very interested lexicographers.
On the other hand the Welsh – at least according to the same dictionaries – seem to regard it as offensive, so is it best avoided anyway? I personally have always categorized it in my head with verbs derived from the words Gypsy and Jew, regardless of whether the etymology is supported. And while I see no good support that welsh comes from Welsh, are there any good arguments that it doesn’t (or why it wouldn’t be plausible) and/or are there any other possible etymological sources mentioned?
Etymologists can find no firm evidence that the verb welsh , meaning “ to swindle a person by not paying a debt " or " to fail to fulfill an obligation , " is derived from Welsh , the people of Wales . However, many Welsh themselves harbor no doubt on this subject and hold the verb to be a pointed slur. It makes sense then to avoid this informal term in ordinary discourse […]
From “The American Heritage Guide to Contemporary Usage” , 2005
Funny thing is that the Anglo-Saxon word wealsc from which we get the name “Welsh” means “foreigner” or “slave” and I’ve always found it odd that nobody kicks up a fuss at calling themselves a foreigner while in their own country and having what would seem to be a super offensive name spread far and wide. *shrugs* But what do I know?
An early example of the “reclaiming” phenomenon?
But probably more plausible that the etymology of the word was just forgotten.
I doubt it was forgotten, just that the Cymry didn’t have the power to make the change. Wonder if they’ll get around to it? Maybe after Scotland defects to the EU lol.
Or that the dominant culture imposes its language.
ETA: replying to @Riemann
Good point. I’m being slow here - I assume that the word in Welsh for the Welsh people is etymologically unrelated?
Yes, “Cymru” (Wales) and “Cymry” (Welsh people) are the same word: com- “together” + bro “country”—loosely, “fellow countrymen.”
It’s certainly not forgotten. “Cymru,” “Cymraeg,” and “Cymro / Cymry” are increasingly used in English, though not very often for Cymro and I don’t think I’ve seen Cymraes in English.
Just to add another tangent, the Perfect Master himself was once taken to task for using welsh as “to cheat”, in a 1992 column.
His response was, of course, exactly as you would expect:
Hmm… I expect snark, that’s more just being a jerk about it, even if the letter was a bit hyperbolic.
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About the only exception is MPSIMS and only sometimes there.
As an American I’ve never heard of “welshing” on a debt. I’ve always heard “welching”. Though apparently both spellings/pronunciations are used.
The earliest entry for the term in the OED, going back to 1860, cited “welching”.
I’d never thought it was offensive because I never knew it referred to any ethnicity or nationality, aside from perhaps the company that makes Welch’s grape jelly.
I finally asked my Welsh spouse. He believes that it does refer to the Welsh people, and that it is offensive. Sample size = 1, and an opinion at that, but something.
You understood his response?
Yes: I don’t understand yours, though.
I’ve never associated welching (reneging) with the Welsh.
A meme regarding Welsh language. It was meant as a joke.
A friend of mine has a Welsh husband. I got it. 
« Welch » is an old, alternative spelling for Welsh:
I have Welsh ancestry, and have always understood this usage to be an ethnic slur.