Thats an interesting question, and I'm not sure it has been covered before. The HE rule states that the strike first regardless of what weapons they are holding, so I would assume that things like Chakax's ability would effect them. However, if his ability gives them ASL, would that not cancel the ASF thus go back to initiative order, where the elves have superior initiative anyway? If Chakax gets ASF as well as giving ASL, I would assume Chakax will go first, but I don't have the book here to check the exact wording.
If two opposing units have the ASF rules, then they both go simultaneously. If a unit has ASF and ASL, they both cancel out each other and go with initiative. pg. 66 BRB. So, in this case, The HE with ASF is given a weapon that has ASL, then yes, they cancel each other out and goes by straight initiative. (or did I mis-interpret the question?).
Which question are you answering? If its the Chakax question, then the HE weapon has nothing to do with it. If its the original question about striking forst with a great weapon, the HE FAQ says the army book overrides the rulebook thus High Elves uniquely still get ASF regardless of what weapon they are holding.
Yes, I beleive I was mixed up on the question(s). My apologies. Meh.. that's what I get for trying to read and answer tiny text using my phone. lol!