The very opening music, including Raoul's section, is played on synth, live. After that, the "Overture" (the chandelier rising) is prerecorded. The first time the orchestra plays live, as far as I know, is when the chorus starts in during Hannibal ("With feasting and dancing and song.") I don't think that's anywhere close to 20 mins.
Other shows that start with pre-taped music include Avenue Q (the "title song" is purely on video) and Kinky Boots (the "Price And Son" theme). I think originally the film music that opened Evita was also originally prerecorded, though I don't know if that's been true for every major production. The original version of Working also started with a rhythmic montage of job-related sounds, which segued into the live band for the start of the singing.
Those who know Bernstein's Mass well will also know that the music at the top was originally played as a quadrophonic recording - the first live playing being the guitar chord for "Simple Song."