this is not a 'scientific' answer but more of an answer based on reason. I'm sure people that are more into IHC have a more detailed and sound opinion on this.
I wouldn't advise you to directly add the PFA to the medium because first of all,the cells should be thoroughly washed before you fix them. Probably you have serum protein in your medium, there's loads of debris and metabolic products floating around in the wells and all of that you don't want to have remaining in your sample.
Secondly, did I understand correctly that you want to directly add PFA at a higher concentration to the well to obtain the appropriate fixing concentration? You wouldn't have an euqally distributed concentration for some time and depending on your well / chamber size the volume might be notoriously difficult to mix and equilibrate properly. As a result, your sample might not be evenly treated.
Angela's response is right on track. A PBS wash certainly improves the esthetics by removing cell debris and the like, but the real need to remove the media and wash with PBS is to get rid of the serum proteins or whatever your source of growth factors is. The concentration of protein in 5-10% v/v serum massively exceeds the protein concentration in your monolayer cells so most of the PFA would cross link serum proteins and generally results in a non-homogeneous fixation in the cells. In addition, your media probably contains free lysine that will also react with PFA making the situation worse.
I wouldn't advise you to directly use PFA on cells. Before fixation , kindly wash your cells with PBS to remove your debris present in cells as well as medium which contains serum proteins. Next you have to be careful about the concentration or time of PFA used for fixation. Most of the ICC and IHC protocols working on 3.7%PFA for almost half an hour at room temperature.