Can I solder a RG316 coax directly to a PCB instead of using the intended SMA connectors?
Soldering directly to the pads of the SMA connector instead of using SMA connectors should work fine electrically.

The obvious problem is that the cable is no longer removable.  If you're fine with that, then go ahead.

It would be good to have some mechanical strain relief if this has a chance of getting flexed.  At only 2 inches wavelength, you do need to be careful about impedance changes over only a few mm.  I'd stay away from adding any material around the solder joint or the wires outside the shield.  However, you can do most anything you want back down the cable a bit from the solder joint and where the shield is still intact.  Perhaps you can hold the cable down with cable ties or something further from the board.