unlikeely, he ain't a yandere
No, he has BPD and Sangwoo is his "favourite person" who idolises and is possessive of though. Bum gets extremely distressed when he thinks Sangwoo has left him. He also does have the capability to cause physical harm, and has done so. Given the theme of this webtoon, it doesn't seem that unlikely that the stress of seeing Sangwoo taken from him in anyway, would cause Bum to behave in the way the OP speculates, or to harm himself as a response.
he mostly deals with stress by self harming.
him causing harm was a result of sangwoo's abuse and him having a psychosis.
i really cant shake the idea of Bum killing anyone who will hurt Sangwoo... its like if he saw Sangwoo got hurt he will snap... or if he see him with somebody else.. Bum wont think twice killing that person who will be with sangwoo seeing him agree to Sangwoo right away... i guess he will do anything for Sangwoo