I don't know of any way to do that, but you can create your own script and attach that to some event on the form, then the script will check all the controls on the form and set a notification if a value is not present.
Here is the code I tried with, probably some cases that I don't handle here, but you get the idea.
function alerter() {
Xrm.Page.ui.controls.forEach(function(control, index) {
if(control.getControlType() === "standard" || control.getControlType() === "lookup" || control.getControlType() == "optionset") {
if(control.getAttribute().getRequiredLevel() === "required" && control.getAttribute().getValue() === null) {
control.setNotification("Some error");
}
}
});
}