I think, like in many situation, the answer is “it depends”. I’d reserve the more intricate embellishment for the spaces in between the singing so as not to clash with the singing. Coloring chords, or something like line cliché, or walking up / down for chord changes are probably fine done with the singing.

The master of chord embellishments and when to use vs not use, is John Mayer. Have a listen to this:

And some of his other songs just involve simple strumming, until he stops singing for a while and plays a cool little solo piece.

Hi,
In general there is no problem embellishing chords while backing a singer (jazz players do it all the time), but as Reuben says, you have to make sure the embellishments don’t clash with the melody.