I guess you would have to ask yourself, do you want to engage into a relationship with a man that is willing to leave his girlfriend so abruptly? If he does so, the action shows a strong component in his character that it is not likely to recede by virtue of entering into a new relationship.
Men are creatures of habit. Change almost always come from within. Outside influences rarely have an impact on a man’s demeanor or actions. If he is the type of guy that will step out on or leave his significant other at a moments notice, he will be that same guy despite whom he is with.
Just a little insight.