G20 and H20 are dates.
To test it, I entered 06/01/12 in G20.
I tried entering dates before and after 06/01/12, and it returned the first condition no matter what.

It will return a blank cell if there is no value in H20 with =IF(COUNT(H20)<>1," ",IF(H20<=G20,"Yes","No")).
Using a "2" returns a blank value when there is a date in H20.