Not exactly.
In Union Cty, you can kill one antlerless deer during the entire hunt. You can kill both of your antlered deer during the hunt, but only one per day. It does not require a special permit during the M/A hunt for the antlerless deer.
During the G/M/A season, you are allowed one antlerless deer during the specified period. It requires a Type 94 permit in addition to the big game weapon license for the weapon you are using.
As far as the antlered deer go, the season and statewide limit is 2. You can kill them during any season that is open, but can only kill one per day. Once you have killed two, you are done for all of the seasons.