The short answer is yes. Although the Festival de Cannes is the 'official' organisation that runs the Cannes Film Festival, it has a long relationship with the main sidebar events. As such, filmmakers are able to submit to all four events, so long as the film meets the submission criteria for each. Although broadly aligned, there are subtle differences between the rules and fees for each event. It's also necessary to make a separate submission to each sidebar.
Whist the various organisations run completely separate submissions processes, there is some co-ordination behind the scenes when it comes to selection. A film will never be selected for more than one event. In the instance a film looks like being accepted for more than one program, the respective submissions teams will liaise to agree who ends up taking it.
Lastly, remember that there only three official sidebars for the Cannes Film Festival: