Hello Timo Karhula
There is indeed a known stream of gas and faint stars between the Milky Way and the LMC, the so-called "Magellanic Stream", as you say, spanning from Carina to LMC, SMC and Pisces-Pegasus-Andromeda constellations (see
http://apod.nasa.gov/apod/ap100125.html). Normally this gas can't be visible (it emits mostly radio-waves), as you say...
When I was near the equator I wasn't able to see any light connecting Milky Way and LMC, also under very dark sky... surely somebody here will have more and more experience of southern sky than me.
TrA-Aps have also their own nebular system, a sort of "Integrated Flux Nebula" similar to that of UMi-UMa in northern sky, belonging to our spiral arm, in the Milky Way Galaxy.
Some of the publications about the Magellanic Stream:
http://adsabs.harvard.edu/cgi-bin/np...pJ...173L.119W
http://adsabs.harvard.edu/cgi-bin/np...ASJ...32..581M
http://adsabs.harvard.edu/cgi-bin/np...NRAS.339.1135Y
http://adsabs.harvard.edu/cgi-bin/np...NRAS.363..509M
But this is the first time that I hear about this phenomenon.