This seems extremely unlikely. Chewbacca is a being of high intelligence, an adept co-pilot and capable of flying a ship on his own, which Saberhagen's aiyan is absolutely not. The image of a hairy creature at the controls of a vehicle was directly inspired by an view Lucas had seen of his own dog sitting in the passenger seat of his sports car. This explains the visual origin of the wookiee race—although Lucas's ideas for precisely how wookiees should look evolved a great deal over the years. Lucas and his designers considered appearances that were explicitly more cat like and more bat like than Chewbacca ended up being. The early concept art for wookiees (mostly by Ralph McQuarrie) does not dog like at all, although the drawings do show ape-like (i.e., human-like) hands.
Early on, Lucas generally thought of wookiees as of human intelligence, but from a technologically lower level civilization—uplifted, essentially. The originally planned climax for Episode VI was to feature a space battle, in which the rebel ships were largely crewed by wookiees. The idea of a mass combat involving wookiees, led by one or more human heroes was a holdover from one of his earliest story ideas for what eventually became the Star Wars saga. However, when it came time to prepare for Return of the Jedi, Lucas realized that, based on what they had seen of Chewbacca in the first two films, viewers did not think of wookiees as culturally primitive, so he was not going to get the effect he wanted with wookiee-crewed spacecraft. Instead, he moved the action to the Forest Moon of Endor, where the clearly technologically primitive Ewoks (note the similarity in the names) took over the role of the rebels' primitive allies.
In contrast, Newton, the aiyin in "Without a Thought" (originally published as "Fortress Ship") is explicitly a pet. It is a smart pet, to be sure—much brighter than Earthly cats or dogs. It can recognize quite long command phrases (such as the entirety of the Gettysburg Address) and follow fairly detailed directions. However—and this is the whole point of the story—it cannot learn or think quickly on its feet. Del Murray has to figure out a way to program his pet's actions to give the illusion that it is learning to play the Berserker's checkers game. Chewbacca, in contrast, may not be particularly good at board games, but it is established early on that he understands how to play them, just like other intelligent beings, and gets angry when he loses, something Newt would never know to do.