No. That will just save an untagged image that's almost certain to be misinterpreted when viewed.
You probably want to Edit - Convert to Profile: sRGB IEC61966-2.1 then Save As your image with an embedded profile. Or use Save for Web and specify the conversion to sRGB there.
But that's not necessarily always the best answer. Who is going to see these images? Are they going online?
Noel, thanks for the prompt response. The images are going to a photobook
company, who require sRGB JPG's. I will process the images per your
If you do that a lot (need sRGB images), you might want to consider having Camera Raw convert directly to sRGB. You get a bit more control over how it fits the gamut of the results into the target profile (e.g., you can move the sliders to avoid clipping, that sort of thing). That's how I work.
Noel, good suggestion. I have tended to print my better images at home,
hence my preference for ARGB. but third party printing, obviously, requires
sRGB. I will keep your suggestion in mind!