when you take off in that situation,do you fly the e/o procedure with both engine just in case???
I would say not. The EOSIDs that I've seen normally have a qualifier attached to them, e.g. ¨Engine failure before 5d/2000' turn left to XXX to hold, otherwise continue to MSA.¨
In extreme cases, following the EOSID on all engines might mean you're unable to do anything but return to the airfield or spiral up in a hold. This isn't the most efficient way of starting off towards your destination! If the terrain is very high on your normal SID, the EOSID may take you in the opposite direction: again, not ultra-efficient.
Also, as .86 points out, you are not going to be flavour of the month with ATC if you do this on a regular basis...