as much as i like to be idealistic as possible, i know this happened to me towards the end of my one and only long term serious relationship. only difference is they (yes, there was more than one girl) weren't "secret" per say. my girlfriend had met some of the girls once before but no more than that. so they knew of each other but not necessarily the impact they had on me. and yes, some of them did want to sleep with me and did attempt to but i didn't cheat. actually, one time, one of the girls fussed me out when i went to visit her about a year after i broke up with my girlfriend. she was claiming i didn't tell her about my girlfriend and that i was hiding her (subconsciously i might have been avoiding the topic, but i wasn't the type to lie about things either so i doubt her story. she just felt that way).
but, some people can do it, some people can't. i wouldn't recommend it for myself because if i have to do that, it usually means the relationship is coming to a close. or perhaps whenever i don't get something i want from my girlfriend, i'd be a lot quicker to cut her off knowing that i have "replacements" in a way. it doesn't help you focus on who you should be focusing on. you start to misplace emotion and give it to someone who you shouldn't be giving it to...