Earlier quoted context omitted.
Yes, Russell definitely did that and was evasive about it afterward. In the late 1940s this insanity was widespread: an entire movement of politically influential players dedicated itself to nuking the Soviet Union before it achieved the bomb and (so the argument went) inevitably used it on us. Von Neumann was another prominent advocate ("If you say bomb them tomorrow, I say why not today? If you say do it at five o'…
Looking at http://www.economist.com/node/699582/print?Story_ID=699582 it seems to be open to some doubt whether Russell was actually advocating a nuclear first strike. (It seems clear that he was prepared to countenance one in some circumstances. That's not obviously completely unreasonable.) After that he went on found the Pugwash conferences, be the first president of the Campaign for Nuclear Disarmament, etc., so…
I'm afraid I don't remember the sources I read (other than Poundstone's book) and don't have time to dig into it just now, though given what I posted I suppose I should. FWIW, my memory is that he was asked about it more than once in the 1960s, denied that he'd said what he'd said, and then responded evasively when presented with evidence of it. On the other hand, my memory is that he'd advocated for a nuclear strike in print; and given the debate you linked to, that seems unlikely.
Edit: My conscience wouldn't sit still until I did dig around a bit. The question is more controversial than Poundstone's book made it seem, so I definitely shouldn't have said "definitely". When will I learn :) On the other hand, there's a lot more material than that Economist article made it seem (the editor of Russell's letters who was defending Russell in that piece really comes across as disingenuous for not mentioning this), and some of it is pretty unpleasant.
The consensus seems to be that Russell advocated threatening the USSR with nuclear strikes to force them to change their policies. Whether he advocated pre-emptive war itself is controversial. He made many comments about this in the 40s and 50s. From a BBC interview in 1959:
BBC: "Is it true or untrue that in recent years you advocated that a preventive war might be made against communism, against Soviet Russia?”
Russell: “It’s entirely true, and I don’t repent of it.”
Other comments were ambiguous (he thought it necessary to "bully the Russians" with the threat of bombing them but hoped it would not lead to war, etc.) Later, he claimed that he had simply "entirely forgotten" that he had ever advocated this. At least two serious biographers, Ronald Clark and Ray Monk, do not find this credible. Here's Clark:
[Russell's] explanation that he had simply forgotten what he had said [...] would be more acceptable if applied to one speech rather than to a long series of articles and statements [...] It might be possible to argue that his disavowal of advocating preventive war was based on the most academic interpretation of the term: that advocating the threat of war unless a potential enemy submitted, even though being prepared to have your bluff called, was not advocacy of a preventive war. But even this questionable escape-route is blocked by Russell’s own statement to [the BBC] and [by] his earlier suggestion that “a casus belli would not be difficult to find".
This paper (a long and convoluted defense of Russell) shows up in Google and contains the salient quotes: http://digitalcommons.mcmaster.ca/cgi/viewcontent.cgi?articl...
My conclusion is that what I wrote wasn't far off, but it was unfair to lump Russell in with von Neumann, Lemay, and the rest of the Dr. Strangelove set who were advocating for nuclear war outright.