Sounds cute, but inaccurate.
If we count the last two planes that are reserved for private use (aka, applications/users can use them for whatever domain problems they like), that would be U+10FFFD.
If we count the variation selector codepoints (used for things like changing skin tone, or the look of certain other characters), U+E01EF.
If we count the last honestly-for-real-written-language character assigned, it would be 𪘀 U+2FA1D CJK COMPATIBILITY IDEOGRAPH-2FA.
But I suppose none of that sounds as fun as an emoji (which are really a very small part of the Unicode standard).