Very hard to say. Also depends on the version of the swiss system used.
In some versions, rating is only used for the pairing of the first round, or first few rounds. In later rounds another criterion is used (typicallly "resistance points", sum of the scores so far of the opponents). There I feel that any difference in pairing strength in the first few rounds should be compensated in the later rounds. [ I believe the system "first three rounds swiss on rating / rest swiss on resistance points" is only used in the Netherlands ]
If rating is used for all the rounds, then there is of course a higher chance of an effect. How big it is is hard to say, for me anyway :-)
I know the basics of the Swiss pairing system, but I also have a question: does the Swiss system show any bias in favor of higher-rated or lower-rated players? In other words, would two players of different ratings but the same strength have different chances of winning the event, given their different pairings?