Won't OM_o steal my visitors?

We don't think so. Furthermore, neither does the IMLS. This study shows a positive correlation between online and offline museum visits, as summarized by this quote:

Researchers have completed the “IMLS National Study on the Use of Libraries, Museums and the Internet,” a study that delves into the use of libraries, museums and the Internet. The study concludes that “the amount of use of the Internet is positively correlated with the number of in-person visits to museums and has a positive effect on in-person visits to public libraries.”