Yup, the fact that it is a progressive disease doesn't bode well for your bf if he refused to admit/deal with is problem.
If you have to ask 'is he an alcoholic?' and you aren't a puritan about drinking then there is your answer I always say.
I like the occassional drink but I hate how I feel the next day so I rarely do it. Just special occassions. My sister loves her evening 'aperitif' (french for evening drinky-poo) but her husband IS French and it is a cultural thing as well. Do I think she has a problem? Potentially yes. That is because I know my sister and her emotional issues. Knowing now what I know about the disease, I am slightly worried as is my mom.
Relationships with someone in recovery is difficult. Only you know if you have the patience and resiliency to ride that roller coaster. I guess what I would recommend is getting the book 'Under the Influence'. There are stickys on SR that you may have already come across. That for me was by far the best source of information on the disease and its progression.