Well, if I know that some star players will miss the next game I will think about my bet twice. And if we adjust our bets depending on the players, for sure these players affect the odds as well. Many factors play a role in creating odds in betting, but I guess we can be sure that the "status" of some players plays one of the significant roles in creating odds.
It is also about the mystification of some names and talents within the world of sports, specially in football/soccer. It just take a look on how Messi dingle handily managed to make the difference within the Miami Inter and its recognition around the world. Sure, a single player does not make a team but reputation cannot be underestimated.
If Argentina was to play in a World Cup, for example, and his star player was not able to participate for whatever reason, I think there would be people who would feel reluctant to bet as much as they planned to. So, yes; I think some single players can move the odds on bookies.
Funny enough is the truth that there's a star player in every team. Some just shine brighter than others.
In my opinion, It is not sufficient to make bookies give odds just to favor a team over another, unless it is that there are more star players, team spirit, in that team, compared to the other team.
If a team has like 3star players and want to play a match against a side with 5star players, it is obvious to say that 5star man team gets great odds.
I also think if a team has been known to produce or harness star players consecutively, it has good impact on their odds following a match bet.