In short, no!
Multiple users can be doing inventory at the same time, but in different locations.
If you try to enter an inventory location that is already ongoing, you will be asked if you want to override their progress and restart that location.
Bar Ejemplo is divided into Bar Fridge, Front Bar and Patio Bar. Here Bar Ejemplo is divided into three locations, so up to three people can do inventory, one at each location. However, only one person can do a location at a time. Otherwise, one would overwrite the others work.