Not a cat in hells chance. Maybe a top end iMac but certainly none of the minis. Check the minimum specs out for the game, your machine has to be on the higher end of hardware.
The minimum spec s on BF3 are bare minimums and only just about playable
here's the minimums
Processor: 2 GHz Dual Core (Core 2 Duo 2.4 GHZ or Althon X2 2.7 GHz)
Memory: 2 GB
Hard Drive: 20 GB
Graphics Card (AMD): DirectX 10.1 compatible with 512 MB RAM (ATI RADEON 3000, 4000, 5000 OR 6000 series, with ATI RADEON 3870 or higher performance)
Graphics Card (NVIDIA): DirectX 10.0 compatible with 512 MB RAM (NVIDIA GEFORCE 8, 9, 200, 300, 400 OR 500 series with NVIDIA GEFORCE 8800 GT or higher performance)
Sound card : DirectX compatible
Here the recommended:
Processor: Quad-Core CPU
Memory: 4 GB
Hard Drive: 20 GB
Graphics Card: DirectX 11 compatible with 1024 MB RAM (NVIDIA GEFORCE GTX 560 or ATI RADEON 6950)
Sound Card: DirectX compatible