Converting to sRGB recalculates the numbers according to the sRGB profile. But you still have to embed the profile itself.
A file with sRGB numbers, but no profile, is untagged sRGB. Such a file will display roughly right on an average, standard gamut monitor - without any icc profile or color management - because the native color space of the monitor is already fairly close to the sRGB spec. In fact sRGB was originally developed to be a description of an average (CRT) monitor.
It used to be common practice to not embed the profile for web, partly because it added to file size, and partly because browsers weren't color managed anyway. Nowadays they are, and in addition we have wide gamut monitors that are nowhere near sRGB, so today I would say you should always embed. At least I do.
Most material on the web is still untagged. That causes problems for people with wide gamut displays, so two browsers, Firefox and Safari, use a neat little trick to overcome this. They assign sRGB to all untagged material, including graphic page elements, and this allows the color management chain to operate again. In fact it ensures full color management for everything (as long as it's created in sRGB) - so you could say we finally have a fully color managed web if you want it. If you suggested that a few years ago, people would just roll their eyes....
