You can be connected to Serial and Network at the same time without any issues. However, you cannot start a label format on one connection and finish it on another. When a printer starts to receive a print format it will not process but buffer data coming in on other ports until the end of the print format is received. It will process buffered data in FIFO order. Many of our newer printers offer a status channel or port for developers to get status while printing but the 105SL does not.
Hope this helps,
Zebra Technologies ISV