There are two issues here. The first is whether there will be sufficient depth of chemical to cover the print. A liter of any liquid is a volume of 1000 cubit centimeters, or 61.0234 cubic inches. If that amount of chemical is placed in a 12x16 inch tray, the resulting depth will be 0.3174 inches if the tray is level. (If your trays are in a sink, the bottom of the sink may be sloped with the result that the trays aren't level. In that case, the depth of liquid won't be constant across the tray.) Therefore, there should be no difficulty in covering a 12x16 inch print with a liter of chemical in a 12x16 inch tray.
Incidentally, when paper is taken out of the package, it has a slight curl (toward the emulsion). As dry paper starts to soak up developer, the curl initially increases, and then as the emulsion becomes soaked, it eventually flattens out. The time for this to occur varies between papers, but can be as long as 15-30 seconds. If you simply place the print in the developer with the emulsion side up, the edges will tend to rise out of the devloper during these first few seconds. If the development time is, say, 2 minutes, it is possible that it might be necessary to fight to get those edges to remain submersed in the developer for as much as 25% of the total development time, and this could result in a perceptable difference in image density along the edges. For this reason, I prefer to initially place the print in the developer face down so that the edges of the print come in contact with the developer during this initial "soak up" period, and then filp the print over to complete development with the emulstion side up. Obviously, this concern is greater when the liquid volume in the tray is small. Note, however, that once the print is wet, all that is necessary is that the liquid depth be enough to cover the print, so as a practical matter this concern is limited to developers.
The second concern is whether the volume of chemical is sufficient to process the number of prints that you expect to produce in the session without exhaustion. In this case, you need to know the manufacturer's recommendation for the number of prints that can be processed in a given volume of his product. The data I have seen has been specified in one of two ways. Kodak used to specify usage rates in terms of the number of 8x10 prints that could be processed per unit of volume, while other manufacturer's have specified the total area (square inches, square meters, hectares, whatever) for a volume. You need to research the specifications for the materials you will be using, and then do the math.
I suspect that manufacturer's specifications are conservative and that you could actually squeeze a few more prints through the process. Obviously, if you process sequentially, the earlier prints will have the benefit of fresh chemistry while the prints at the end of the run will be working against partially exhausted liquids and it is possible that the difference could be perceptable. One approach to addressing this is to increase the processing time as the chemical becomes exhausted, but that's a pretty experimental approach. Alternatively, you can compensate for this by processing all of the prints at the same time - but then you have to revisit the issue of the depth of the liquid in the tray and the fact that it can be a pain try to shuffle a bunch of prints in tray that is the same size as the prints you are processing.