Android updates have nothing to do with what network the phone is currently on, or what SIM card is inserted. The updates come from whoever you got your phone from.
If you bought your phone from a carrier, they almost certainly customized the OS to include their special apps (a.k.a. bloatware), and sometimes to limit features like Wi-Fi hotspot. For that reason, the updates have to come from them, and of course this adds some delay to the process: once the manufacturer has the update ready, they supply the new source code to the carrier, who has to update their special features for the new version, and go through another round of tests and QA. Carriers don't have the same software expertise or resources as OEMs, so this takes longer.
If you didn't buy the phone from a carrier, then it'll be running an OS provided by the manufacturer, so updates will come from them directly. For Nexus devices, this means the updates come straight from Google.
In your specific case, if your Galaxy Note came without a SIM card, I guess you didn't get it from a carrier, in which case you'll get the update from Samsung, as soon they make it available for your region. If you did get it from a carrier originally, you'll get the update from your old carrier. Either way, your new carrier has nothing to do with it, because they didn't provide the OS in your phone.