I will answer that a bit indirectly. Catholic church has "ex opere operato" principle which means that sacraments "work" if they are performed in an appropriate way by an appropriate person. By contrast, Eastern Orthodox church is on the "ex opere operantis" side, which means the sacraments are valid depending on the internal spiritual state of the receiver.
So that means there is no direct answer. It is possible that with the right disposition of the receiver, protestant Communion would have the same spiritual effect on the specific person as Eastern Orthodox communion, but it's impossible to tell for anyone (when it comes to the spiritual side).
When it comes to the canonical side (human law) - obviously Eastern Orthodox church believes that their rituals provide the best conditions for the Communion sacrament to be performed correctly, thus having the best chance to have a good effect on the recipient. Some churches accept sacraments from different denominations, some don't, but it's more of an organizational issue.
Spiritually there is no direct and sure answer, because the real effect is only known to that person and the God Himself. The only way to know if they "work" in the same way would be to judge the state of ones spirit after the sacrament, which is an impossible thing to do for humans (and attempts to do so are strongly discouraged "Matthew 7:1 Do not judge, or you too will be judged").
I think the general Eastern Orthodox approach to such spiritual matters is "Do not resent. Do not react. Keep inner stillness" (from Philokalia).