If I just place the components used in kicad in the PCB editor, does the free to outing plugin do all the routing work seemlessly?
Good placement is 90%+ of the work.
Good footprint placement is indeed very important, but not 90%.
Another important part is knowing how to design a good PCB, and there is more to that then only the footprint placement. (Assuming a correct schematic) the next item on the priority list is the GND zone. Nearly always a full GND zone covering the whole PCB is ideal, but this is not achievable. Punching holes in the GND zone for other nets is normal, cutting the GND zone to pieces with long tracks (as most autorouters tend to do when they are not properly set up) is very bad.
After that, it gets more complicated. For digital logic, you can usually accept a few hundred mV of noise on signals, while in some analog boards microVolts may be unacceptable, and also voltage drop over tracks can be of a huge importance. Consider for example a 10mOhm high current shunt with feedback sense wires. The copper of the PCB can have a higher resistance (and varies with temperature) then the shunt resistor itself. So this needs careful design and use of net ties (which brings us back to footprint placement).
Freerouting (and autorouters in general) are a recurring topic. I suggest you dig up some of the old threads and read them. You can start with:
No.
If you place the footprints where you require them on the PCB then use an autorouter for the tracks, usually, at best you will have to tidy up the result, and at worst, you will have to start again.
Autorouters are generally a very poor substitute for the human brain.
It looks for me like you are writing about % of knowledge while retiredfeline was writing about % of work. I also think that placement is about 90% of work, but this my opinion comes from 2 layer PCBs where I need a lot of time to place all footprints to then allow me to connect everything at top having whole bottom to GND. For 4 layer PCB placement is simpler as you than have 3 layers for connecting everything except GND.