Here's how I do it:
When I want to soft proof an image, I go to View>>Proof Set Up>>Custom. In that pull down I select my paper profile, and rendering intent. Then I hit the 'OK' button. When I am done evaluating/editing the image, I go to back to the 'View' menu item again. However, you will now notice that the item right below 'Proof Set Up', called 'Proof Colors', now has a check next to it. Simply click on 'Proof Colors', and it automatically disengages the soft proof you turned on earlier. Whatever the case, any of your your selections in the 'View' menu has no effect on how your file gets tagged and saved.
If your incoming image is already an AdobeRGB image, you are good to go. If it is another colorspace, you will need to 'Convert to Profile' to Adobe RGB. (Then make sure that when you save your image, the check box that reads 'embed profile' is checked.)
Regarding your last question, unless you have a very large gamut image, and are viewing on one of the new wide gamut AdobeRGB capable monitor, you will not really see any difference soft proofing that AdobeRGB image in sRGB, as most monitors are only capable of displaying a gamut similar to sRGB anyway.