It may work but you will not be able to run any useful application with such a setup.
You can read mail and news with such a setup but you'll not have fun with CAB.
I do not even think that it will work when a STIK compatible TCP stack is loaded into the small amount of memory (what 1MB surely is even on the ST).
If you manage to do it - drop me a mail.
I'd be interested to connect a 1040STFM as a net terminal via slip (or PPP) over nullmodem to my Linux box.