Sorry for the delay in answering this. Somehow my email notification for new posts didn't work.
Anyway, no, TeSSH only works with the Telnet and SSH network protocols. It does not work with direct serial connections. Working with serial connections is really a whole different ball game compared to network connections. However, you might be able to find some software that bridges between the two and might provide a local network interface to your serial ports. Try googling that and see if you can find something. If not, then you are stuck with old terminal apps, sorry.