I don't think it matters but I'm running Klipper as the printer firmware.
With some more testing what you say makes sense, including the part about printing from the SD card. Though if I do a print that way and disconnect & then reconnect the information doesn't update either though the print obviously runs to completion
I guess what is/was puzzling is that if I do a "soft" disconnect by closing the browser everything continues to run even though OctoPrint has no place to send the updates. I'm also running TouchUI on the display connected to the RPi so don't know how that factors in there. Though the Touch/UI interface shows "Offline" when I disconnect via the browser.
I'm fine with the data stream going away so long as I understand the behavior and can provide answers or explain the limitations to any other users. I may need to add some additional code to handle the unexpected scenarios as well as capture some of the printer events I'm currently ignoring.