One of standard parts of handshake between device and mobile network is exchange of IMEI number (not mandatory but most networks do) ... IMEI is a unique number identifying device, first part identifies device manufacturer and model.
The more important part of hanshake is sending device's capabilities to serving network. The capability list doesn't identify device though, but it helps network to offer optimum services to every connected device.
So, yes, network would know that SIM card was not used in a phone. It's up to MNO to act on this information, odds are that if it works initially, it'll work at least for some time ... MNOs usually don't look after individual customers not adhering to rules, they just implement filters in their network. They might implement new filters from time to time ...