For anybody looking for an answer, it is possible to use Ajax to update the values of an autocomplete object in MDB. In the example below my Ajax response has filtered the result already, so javascript no longer handles that part (but you can add it in if required). The Ajax response returns a simple array of items based on the search text that was fed in. Also note, this is vanilla Javascript, no Jquery required:

 var xhr = new XMLHttpRequest();
 var isAjaxWaiting = false;
 var dataList = [];  //This will hold our updated data

//this function creates a delay 
const wait = ms=>new Promise(resolve => setTimeout(resolve, ms));

 //Init the search
 function initSearch(){
     const obj = document.querySelector('#search-autocomplete');       
     new mdb.Autocomplete(obj , {
         filter: getUpdatedData
     });
 }

 //send search text to ajax and keep looping until we have a response
 const getUpdatedData = async (txt)=>{ 
     if(txt!="" && !isAjaxWaiting){
         sendDataToAjax(txt);
         do{
             await wait(300);    //this forces a pause for 0.3 seconds - will loop if ajax hasnt returned yet
         } while(isAjaxWaiting)
         return dataList;        //Once do/while loop is broken out, return global dataList
    }else{
         return [];
    }
}

function sendDataToAjax(txt){
    isAjaxWaiting = true;
    xhr.open("POST", "/ajaxurlhere", true);
    xhr.setRequestHeader("Content-Type", "application/json;charset=UTF-8");
    xhr.send(JSON.stringify([
         "searchtext" : txt
   ]));
}

//Update global dataList when Ajax is returned
xhr.onreadystatechange = function () {     
      if (xhr.readyState === 4){             //4   = DONE
         dataList = JSON.parse(xhr.responseText);
         isAjaxWaiting = false;               // Our do/while loop will be able to break now
     }
  };