Interesting. That was not my experience. I could type to search, but pressing enter just showed a message about copying the emoji to the clipboard. This was over a Remote Desktop connection, so perhaps that affected the behavior? Or it might depend on the specific type of text input field.
In any case, most of the characters I use XCompose for (such as arrows, mathematical operators, Greek letters, and non-ASCII punctuation) are not emojis and cannot be selected this way.
This is so nearly awesome, but the hint only works for emoji. So I can type "<WIN>+. sad <ENTER>" for a sad emoji but, e.g., "<WIN>+. gamma" doesn't find the Greek letter. There seems to be no way of selecting a symbol using only the keyboard. So I go back to charmap. Its shitty UI hasn't been improved in decades but at least it can search all of the unicode characters.
In any case, most of the characters I use XCompose for (such as arrows, mathematical operators, Greek letters, and non-ASCII punctuation) are not emojis and cannot be selected this way.