Rocker Melissa Etheridge will play a one-week stint in “American Idiot” next month, stepping into the role of St. Jimmy.Part is currently played by Green Day frontman Billie Joe Armstrong in a 50-perf engagement. Etheridge will fill in during a week when Armstrong is out of the show, with Armstrong returning to the role for another three weeks afterward. In the stage adaptation of the Green Day concept album, Etheridge takes on the role of St. Jimmy. Although the role functions as something of an alter ego to the young male protagonist, the gender switch won’t necessitate major changes to the tuner. The scheduling of Etheridge engagement, as well as the Armstrong stint, aims to attract business to the tuner during a winter period that is traditionally hard on Broadway box office. Last week “Idiot” was particularly hard hit by the seasonal drop, with weekly B.O. down some 35% to about $620,000. Etheridge will appear in “American Idiot” Feb. 1-6, with Armstrong resuming perfs in the show Feb. 10-27.