They could have had the same effect killing Chakotay. Killing Chakotay would probably done a better job overcoming the mediocre state of Voyager at the time. And I doubt the Voyager fanatics would have complained about losing Chuckles. He was more involved in the Voyager books at the time and wasn't the icon Janeway was.
But killing characters wouldn't be necessary at all with quality stories and authors. The good publicity of Beyer's high quality books would have rejuvenated interest in itself. I'm in a similar state in that I'm done with Ent. I still like Ent, but I wouldn't go back unless they get a decent author and story in there. No need to kill Archer.
If they killed Chakotay, I doubt anyone would notice. It would be right up there with killing Travis Mayweather, or the second nameless redshirt from "The Apple"