Probably. There's overwhelming evidence (in general; not web specific - but I'm not aware of any research which shows it doesn't apply online) which shows advertising context is critical in market positioning.
Have a look at the Tesco-Levi lawsuit from a few years ago, Levi a premium jeans company sued Tesco a supermarket to prevent it selling Levi jeans, because putting premium jeans alongside vegtables damaged the exclusivity of the Levi brand.
While I appreciate the example is from a different context, I believe there's no reason that the same principle don't apply online.
Another way of looking at it - think about the following scenario: Say a consumer was looking at a porn site and it contained an advert for a dating service (called A), and later on the consumer looked at their church's website and it also had an advert for a dating service (called B). If you questioned the consumer about which dating service was more "wholesome" I'm willing to bet the consumer would pick B over A the vast majority of the time.