In most recordings of baroque concertos that I've heard, the soloist plays straight through without stopping, especially in the first movement. While there are marked solo sections where the soloist is more exposed, but she plays the whole time.
One exception to this that I've found:
However, is this the exception or the rule?
In Classical/Romantic concertos, there are often long orchestral introductions and many tutti sections where the soloist stops and awkwardly holds his instrument/fiddles with it/stares silently into the crowd with intense eyebrow movements. Is this also part of the style of the day?