There would be no problem with an E-3 coordinating a major SAR effort - the sensors, communications and datalink fit are all fully compatible with what is needed. Indeed, the E-3 trains for and has been used operationally in overland CSAR. As high level (30,000 ft) top cover for C3, it has no equal. However, SAR visual search is impossible and the E-3 has no bomb bay to drop equipment from so it does have its limitations.
The main problem is that the E-3D is not scaled for SAR operations. There are insufficient airframes and trained crews to maintain NATO tasking and also to run a standby commitment. The E-3 takes quite a big lead time to get airborne without prior notice and therefore could probably only be useful if already in the vicinity. I will add (and I have stated this on many other threads) that the E-3D is tasked by NATO and the RAF does not have the authority to routinely place an E-3 on standby for SAR (ask the SOs who used to ring Waddington to ask for an E-3 to be placed on QRA to be told to contact Force Command at SHAPE where it was regularly refused because there was an E-3A on alert at GK).
The E-3D has successfully achieved maritime tasks, including counter drugs and SAR in the past - it is just an impractical aircraft for SAR standby commitment - technically, operationally, and currently financially. It could be used in such a role, but it would take a big increase in funding, training, and resources to make it effective.