Do CNAME DNS entries affect SEO?

Using a CNAME does not impact search engine ranking. It is common practice to use a CNAME. A classic way of setting up DNS is to have (servernames).company.com and then create (servicenames).company.com as CNAME's pointing to server names (where service names are fx "www").

If your DNS setup is particularly convoluted and it takes a looong time to resolve your DNS hostnames, then you could maybe rank a little lower with services like Google Adwords. Adwords takes the site 'quality' into account, and speed is a part of this. Generally DNS lookups are quick, so I think this is highly unlikely to be an issue.