"Connection to" runs the gamut from friendship to business relationship or whatever while "attraction" usually is connected with some emotional response and is one step beyond a simple connection. So if I was attracted to a woman because of the charm of her personality or physical charms, her quality of character or the manner in which she treats others, I would want a date. Other than that, the answer would be, No.
Friendship might be better, less odds of becoming awkward later in life in the relationship didn't work out.
No...that's called a friend.