I can hear it in the song, but he doesn't clearly pronounce the ending constant so it sounds like "an" instead of "and" "an my girlfriend went and cheated on me"

"wenッ- ン - cheated". Sounds like "wen "chisai tsu", "n" , "cheated"

And therefore, if the weak form of "and" is simply "n" -- as it very often is -- then this lonely "n" sound would be assimilated to the "n" sound at the end of "went" (the T is not typically released after N at the ends of words). Thus "went and cheated" would sound like "wen'ncheated"

Yes, "and" can be very weakly, almost imperceptibly, pronounced. It is one of a set of words called function words. Function words include conjunctions, articles, pronouns, prepositions, adverbial particles, etc. these words always have a strong pronunciation and also one or more weak pronunciations. A good dictionary, such as Cambridge, will show you both (go to Cambridge's online dictionary and look at the entry for "and"). Weak pronunciations are much more common than strong. I almost never say "and" with a strong pronunciation. This is true in every dialect of English, and it is not informal.