No, indeed, it is not supported. It will be implemented in a future version. Meanwhile, you can use the special "\zs" modifier in the regexp, which changes the start of the match to the position where it appears. Thus, you can do what you show above in this way:

  y/everybody\zs/

The used regexp is "everybod\zs", which works exactly the same as "everybody", but when a match is found, the "start of match" is artificially changed to after the "y".

This is actually a vim feature, which ViEmu does provide. There is also the "\ze" modifier, to override the match-end. You can use both:

/before-stuff-\zs.*\ze-after-stuff/

This regex will only match at strings starting "before-stuff-" and ending with "-after-stuff", but the only text highlighted/selected/replaced/yanked/etc  will be the "meat" in between.