[SalesForce] Getting the value of an inputField on the page

You could wrap a script in an outputPanel and rerender it on every save. Then you'd have the most up-to-date value of the variable. eg:

<apex:outputPanel id="saveResultScript">
    <script>
    function confirmProceed (){
        var dataSaved = "{!JSENCODE(dataSaved)}";
        if(dataSaved == 'false' && !isDirty) {
            if(confirm('Are you sure you wish to continue - any unsaved changes will be lost.')) {
            }
        }else {
            return false;
        }
    }
    </script>
    </apex:outputText>
</apex:outputPanel>

Outside this block we have another script tag which we'll put the isDirty variable (so it doesn't get rerendered on save)

<script>
var isDirty = false;
</script>

As long as this entire panel is rerendered on every save, we can check the newly updated dataSaved variable and the locally updated isDirty variable (you said you had a variable that performs this function on any onenter event)

This way, we don't need to talk to the controller for confirmProceed to work. Hopefully this helps a little. I feel a little unsure of your requirements, but this is something that I have done several times myself and it works pretty well.

Oh and using a RemoteAction as suggested in the comments would probably work too, as long as you keep in mind that RemoteAction methods need to be static. They definitely return a value immediately for you to act on.

Update One last thought - you could use a RemoteAction to save your data and then (depending on the result) call an actionFunction to update the dataSaved var on the controller non-statically - while you can do what you want without waiting for a rerender - this should be very performant.

you should consider using a change handler instead as pointed out in the documentation:

component.cmp

<aura:component>
    <aura:attribute name="status" type="String" default="open"/>
    <aura:handler name="change" value="{!v.status}" action="{!c.handleChange}"/>
    <lightning:select aura:id="select" name="select" label="Opportunity Status" value="{!v.status}">
        <option value="">choose one...</option>
        <option value="open">Open</option>
        <option value="closed">Closed</option>
        <option value="closedwon">Closed Won</option>
    </lightning:select>
    <lightning:button name="selectChange" label="Change" onclick="{!c.changeSelect}"/>
</aura:component>

controller.js

handleChange: function (cmp, event, helper) {
    //Do something with the change handler
    alert(event.getParam('value'));
}

and for future reference, feel free to refer to the official documentation for examples and component usage. =)