Absolutely. Web images should be posted as sRGB. They will never look perfect, but most viewers will have a good idea of what the image looks like.
Never assume that viewers can use, or even understand, colour-managed software, or that such software, even if in use, works well enough. In particular, avoid using ProPhotoRGB or similar wide gamut profiles because they more often than not will lead to bad web renditions for the majority of viewers.
Colour management becomes paramount when you publish images to books, or magazines, or want the best quality for exhibition prints. Always communicate with the guys who do the pre-press stuff to ensure your image will end up as you intended.