I would never use an ampersand in either context. I have more style than that.
All seriousness though—this pedant appreciates you giving me an English grammar rule to brush up on. My pronoun work has been strictly en el español of late.
GP is probably thinking of "My dad and me"; not sure how far back it goes but I've certainly heard it quite a bit from native speakers. You might hear someone say, "Him and me, we go way back", but that's slightly different; but "Him and I" mixes the subject/object case, which must be wrong (and I've never heard before).
ETA: I generally don't bother "correcting" the grammar "mistakes" that native speakers make (like "My dad and me did X"); but if I think it's pretty clearly a non-native speaker, I'll correct them, because that's what I would want someone to do for me if I were speaking in their language.
I always hated this because English is not so simple. To my eye, “me and him went to the store” or “him and me went to the store” both sound good to my ear. But “he and I went to the store” sounds slightly weird, and “I and he went to the store” just sounds awful. Which makes me think this rule is bogus, and that when you compose pronouns with “and”, English actually prefers the object case even when in the subject position. If it were as simple as the rule you suggest, the order of the pronouns would not matter. I’ve also heard people say (e.g.) “he did it with X and I” which makes me think “She and I” in the subject position (for example) is more of a prescriptive grammatical virus than actual English.
