There may be a slight color shift for others using IE on cheaper monitors and IOS devices but not as extreme as IE on a wide gamut monitor. Most people do not use high-end monitors such as these so there is little to worry about. Give it a try.... and for the post above do not set your workspace to your monitor profile it is wrong. and yes save to web and select "convert to srgb" and "embed profile"... let us know how it goes.
PS after you install Firefox come back and view the two images I posted. If you see a color change between the two than the browser is reading them correctly
If FF does not perform as expected, folow the link below and scroll down to "HOW TO SETUP & ENABLE VALUE 1 FULL COLOR MANAGEMENT IN FIREFOX:"
BEST FIREFOX TEST PAGE How To Enable FULL COLOR MANAGEMENT of ICC Profiles in FF31 Fire Fox thru FF 3.6