No I could not be friends with the protagonist (Dorian). Maybe for a short while in his early life, but I would not be able to sustain the relationship. I think I could if I met him just after his picture had been painted because he was a handsome and charming man that could get anything he wanted form anybody with his charm.
A reason for why I could not be friends with the Dorian Gray is that he would cause me jealousy because of his good looks, his youth and his charm, to get whatever he wants, even when I have grown old and my youth and looks have left me. While he could still chat up and charm the young and old alike, I would be stuck in the corner talking to myself.
Thirdly I would not be able to be friends with Dorian Gray is because near the end of his life, he created a bad reputation for himself, which in turn would corrupt my reputation as well and cause all my friends to hate me. Which would lower my social status and destroy me socially.
The possible case where I would be friends with him, such as Lord Henry, I do not think that I would last long. I think that his influences would devour me and I would become corrupt and crazy. His charm would have too much influence on me and I would become a extremely happy false version of myself. Then when he tires of me and my personality he would throw our friendship away like a piece of trash. This would probably destroy and I would go into a deep depression and would lose myself.
So to summarize I would in most cases not be able to sustain a relationship with Dorian Gray, because like everyone else, I would fall to his charm and influences.