Or will the carriers detect a "foreign" SIM card and block access, similar to how my AT&T phone won't work on a Sprint cell network.
Actually, this particular instance is not a case of Sprint rejecting a Ma Bell SIM card, it's a case of two entirely different wireless technologies. AT&T and T-Mobile in the US run on a more globally accepted standard, known as GSM. However, Verizon and Sprint run on a faster, but less accepted, standard known as CDMA. These two are incompatible with each other; your AT&T phone won't work on the Sprint network because it speaks the wrong language.
What the gods would destroy they first submit to an IEEE standards committee.