Yes , you can play Battlefield 4 on custom settings with radeon hd 6670 DDR5 (ddr3 is quite slow)..
These are my settings -
Resolution - 1360 * 768
texture quality and filtering on ultra
No AA , No Vsync ,No AO(or you can set to SSAO doesn't make much difference)
and rest all are on medium settings..
Benchmark - min - 29 max 43 average - 31