Originally Posted by
rudestuff
Short answer No. But it makes sense to let them know at the earliest opportunity, preferably before you depart the SID.
In the US, ATC don't know what your Engine Out procedure is. You are, by definition using Emergency Authority. Climbing straight out of ATL for example, and not following the SID. Chances are they've seen you're having a bad day, but any coms are 'time permitting'.