Is it possible to connect an ubuntu laptop to a USB-C docking station over a USB-C to USB-A adapter and get signal in the monitors?

No. You can't. It's hardware that is missing. USB C on many laptop supports USB C Alt mode which is DP over USB C cable.

The sound is however a normal USB signal, and thus works perfectly fine over USB.

It is hopeless.

Your USB C dock expects a video signal over the USB C cable, but your USB A to C adapter only repeats the USB 2.0 signals. Some also handle USB 3.0 signals.

To make your dock work, you have need an USB A to C adapter which has a graphical card build in to re-create the missing video signals from a standard like displaylink. If these would exist, they would cost about the same as a dock. (The reason USB C docks are cheaper, is because they don't need to convert the video signals