No, this is currently not supported by Saros. While it would technically
be possible to add this functionality, it is not something that is
currently being worked on.
If sharing the console output is necessary for your development process,
I would suggest additionally using a screen-sharing tool.
Otherwise, I would suggest having a look at other collaborative
programming tools. I think a shared console is supported by VSCode's
"Live Share" feature. Or you could have a look at the "Code With Me"
extension for IntelliJ IDEA.