If one counted the omer before saying havdalah (or even 'hamavdil bein kodesh l'chol), does the omer count?
Not sure if one can bring a proof from this, but the Ashkenazic minhag is to read the Megillah after Havdalah (The Bei’ur HaGra 693:1 explains that we recite Havdalah after the Megillah in order to delay ending Shabbat as much as possible (see Pesachim 105b). Pri Megadim M”Z 693:1, Mishna Brurah 693:3, and Nitei Gavriel 28:8 agree. from http://halachipedia.com/index.php?title=Reading_the_Megillah#cite_note-24)
so perhaps one is indeed yoe'tze with the counting of the omer before havdalah/hamavdil.
See O.C. 489:9 - On the conclusion of Shabbat and Yom Tov, one counts before havdallah. The reason for delaying the Omer is to lengthen Shabbat as much as possible.
If you're wondering if this seems contradictory (i.e., how can you count for the next day when, apparently it's still Shabbat, based on what I just explained), we are relying on the havdallah that was already said in the Amidah. See p. 136 in this book.