Replacing Antennas for Wireless Communication
Good news: Yes, you can get rid of the SMA connector and the antenna. 

Then you can use a chip type antenna or just a piece of wire with the right length. 

But you will have to match this new antenna to 50 Ohms for best performance. This was done with the 3 small SMT caps that you see on the picture right before the SMA. You will have to find new matching values and this is done with a VNA network analyzer. But if you can live with a few (like 3-6) dB loss, you might get away without matching and just connect your new antenna right to the PA. 

Edit:
Ok, i got from the datasheet that operating frequency is 2.4GHz. This calls for a lambda/4 monopole antenna which is 3cm long (standing 3cm rectangular to the GND plane). Such an antenna has a (real!) impedance of 36 Ohms, so you won‘t loose much of power if you do not provide the right matching elements.