Paragon Wiki says they don't, and I don't have a Widow high enough in-game to check, so I will defer to the Wiki in this matter.
@Demobot
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That's a bug in Mid's.
Epic ATs don't have access to either the ancillary nor the patron pools,
but Mid's is giving Soldiers and Widows access to the Brute versions.
6000+ levels gained and 8 level 50's
Hello, my name is Soulwind and I have Alt-Itis.
It is not a bug.
Widows get the same pools as Brutes.
Alts on all servers, lvl 50 of every AT:
lvl 50 Heroes on all servers but; Pinnacle, Victory
lvl 50 Villains on all servers but; Guardian, Pinnacle, Triumph, Victory
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There seems to be uncertainty... I guess I'll respec mine and find out.
Really? I could of sworn they didn't.
OK, I stand corrected then. 
6000+ levels gained and 8 level 50's
Hello, my name is Soulwind and I have Alt-Itis.
I tested it, and they do not have access to the hero ancillary pools. (they do get the brute pools but I knew that already)
Yeah, SoA get PPP but not APP. Khelds get neither PPP nor APP.
Honestly, I think it would be interesting to see what would happen if those pools got opened to EATs. However, I doubt we'll see it any time soon, if at all.
Just a sanity check here. I was under the impression that arachnos widows don't get access to hero ancillary pools. Yet mids seems to think they do. They don't, correct?