Republic is, well, set during the waning days of the Republic(starting around Episode I if you count the ongoing series not named republic before it) through Episode III, where the series meets up with the Empire series.
And yes, if I'm not mistaken, they are right there with the EU as "canon."
Even more so now that Quinlan Vos was mentioned in Episode III(a main player in the ongoing "Star Wars"/Republic series since around 2002).