Microburst 2002
I think that answer is rather too simplistic. Take an example where you have just departed an airport at maximum TOM and suffer and engine failure/fire, say one that won't extinguish. You decide that you want to return immediately to the same runway at the current weight/mass.
A quick check (or even better a slow one before departure) shows that yes, you can stop on that runway but in the event of a missed approach you cannot meet the E/O gradient. Its now up to you. You may be able to come up with an alternative missed approach procedure which MAY or may not be the same as the EOSID you had just used 10 minutes ago. The primary goal being to conduct a MAP safely avoiding all terrain and of course you must get ATC approval before commencing the approach (maybe too late if you call for it during the miss).
A word of caution though: MD83FO I really hope your company has checked that such EOSIDs are appropriate for the airfileds at which they wish you to use this procedure. An EOSID has nothing to do with a missed approach whatsoever as they are both flown from geographically different locations e.g. 2 nm or more difference. However it may be the case at certain airfileds it will be perfectly possible to safely follow the EOSID during a miss, whilst at others it may well not.