Doesn the existence of two blocks of Greek characters create problems for searching in Greek?
No. If you examine the code charts for the U+1F00..U+1FFF block of “extended” Greek carefully, you will note that all the polytonic Greek pre-composed characters have canonical mappings. This means that they are canonically equivalent to sequences consisting of the basic letters plus sequences of the basic letters plus combining voicing and accent marks. Any properly constructed Unicode search operation should treat canonical equivalents the same, so it should not matter whether one specifies a target match in terms of the pre-composed characters or in terms of the sequences of basic letters and combining marks. This situation for Greek is no different from the requirement for the Latin script that a search for a pre-composed Latin letter and the same letter with a combining accent mark produce the same results.