Bradley Cooper has been described as someone who does have a sex appeal and People magazine apparently named him sexiest man alive in 2011. Cooper himself was at first uncomfortable with the title but later found it amusing. Bradley Cooper has also been in a relationship with at least five women since 2006 which could be a sign of him having a good physique though it could also be his personality. Albeit, the one woman he married divorced him later that year. Nonetheless, Cooper has said that he gets along with people and this is probably another reason he is popular rather than his good physique.
Cooper is considered a fairly good-looking actor by many and is often stared in roles which require him being an action man. This could be a hint at how he is perceived. As far as whether he is actually healthy, you will have to ask his physician.