Yeah, it's a case-by-case thing. Typically a couple of years for most musicals, I'd say. Some are less, some are more. Many don't see full productions.
And there isn't a real, set "workshopping" phase. Sometimes shows are mounted, then undergo more workshopping, then are remounted. They could be workshopped and then see no further work of any kind, other than quiet rewriting, for years- and then suddenly resurface in industry readings. Sometimes shows are commissioned by a theatre company and are bound by a schedule.
There's not a set path to the final product. Sometimes shows are written and move right to a major production with minimal workshops/showcases/readings. Sometimes they languish.
"...everyone finally shut up, and the audience could enjoy the beginning of the Anatevka Pogram in peace."