Chrome will simply apply the current monitor profile. But your Adobe RGB file will at least not look horrible. But even with the monitor profile applied, Chrome does not seem to support embedded ICC profiles.
And when Chrome updates itself, as it does often, it will typically erase your " --enable-monitor-profile" modification without telling you about it. So you have to keep on top of it which seems counterproductive at times. I guess when you only have a few hundred programmers working on a project it would be pretty to turn this into a persistent checkbox somewhere, or do something as extreme as adding basic color management.