On the whole, all double tracked lines are nowadays signalled for bi-diectional running, yes. However, Germany has still many lines with missing left-hand home signals. And there are, AFAIK, big differences between its use.
For example, in Germany, typically block signals are present only on the right track, and there are no starting signals on the left-hand through station tracks even on new lines; this makes running on the left-hand track quite cumbersome; still, on the heavy-traffic Munich-Rosenheim line, there was more or less planned left-hand running up to a few years ago - but then, for reasons I don't know, it essentially stopped.
In Austria, it is used "without hesitation" if it helps a train to gain a few minutes.
For other countries, I don't know (if the above counts as "knowledge") enough to say something substantial.
H.M.
