i'd suggest getting an extra 4gb of ram. BF4 is a ram hog. With only 4gb you will be writing to your swap file a lot, which will slow the game down at certain times.
Your GPU is really only entry level and with 1gb of vram your limiting yourself too. As nouvake has pointed out, it will depend on what res your gaming at, but with two upgrades (more mem, and a beefier GPU) you could be playing it on high with no problems, with really goof FPS.
As it stands, i'd say low to medium settings, 40-60 fps, depending on which map. Silk Road and Operation locker, seem to be the least demanding of the maps on BF4, and something like Siege of Shanghai is very demanding.
Yes of course you can. That 7770 is capable of playing bf4 ipto 1600x900 on tweaked high settings if it paired with a good cpu with good fps. You have a good cpu but as your gpu has only 1gb of memory the best setting for you is: 1366x768 with high settings with no AA or maybe 2x AA. You will get 40-45 fps for sure
Note: increase your ram to 8gb. It not only help increasing your in game fps but also reduce the load time of the maps cause its a very demanding game especially the operation locker 50+ player servers