No.

You can only check it after a match. You can always do one dominon Co-OP (8min ~ 10min)


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## EDIT ##

With the new patch (Hecarim) they change it:

> Added first win of the day status to the summoner profile.

[hecarim-patch-notes][1] And here the [perm link][2] from wiki


  [1]: http://na.leagueoflegends.com/news/hecarim-patch-notes
  [2]: http://leagueoflegends.wikia.com/wiki/V1.0.0.138#PvP.net