I am designing a PCB which has a chip antenna with a coplanar wave guide. Having a 4-layer PCB (stackup layer: rf signal, GND, POWER, signal) can I run traces across the antenna transmission line on the farthest bottom layer?
Yes, you can run a trace on layer 4 in this scenario. The ground layer on layer 2 means that all field lines from the transmission line are terminated on layer 2, and anything that happens on layer 4 will have practically no effect on the transmission line.
If you are spacing your fencing vias as close as shown in the diagram, you might end up having to skip a via to make room for the layer 4 trace to pass. If you're working below 10 GHz, I don't expect this will create a significant problem. Even at higher frequencies, a single skipped via in the via fence is not likely to cause a noticeable problem (but of course you could do an EM simulation to be sure if your application would be sensitive to a tiny increase in loss or degradation in return loss)