Yes it is possible to disable the drag option. From my investigation, there are 2 ways you can disable it.
Solution 1: Comment Out Javascript
You can disable the drag and drop feature by commenting out the method initialize in the javascript.
Navigate to the \Website\sitecore\shell\Applications\Content Manager\Content Editor.js
.
Open the Js file and search for var scContentEditorDragDrop = Class.create({
Comment out the code. Please see below

Solution 2: Custom pipeline
You can implement a pipeline and add it to the <uiDragItemTo>
. When dragging item starts, it will check if the item can be drag or not. Below is the sample code snippet
public class Draggable
{
public void IsDraggable(ClientPipelineArgs args)
{
Assert.ArgumentNotNull((object)args, nameof(args));
// Logic to check if dragging item is enable
// if yes, show dialog and abort pipeline.
Context.ClientPage.ClientResponse.Alert("You cannot drag an item. Feature is disabled.");
args.AbortPipeline();
}
}
When the item will be drag and drop, the below error message will appear and it will not drag the item.

You need to patch the config so that your patch is in first order.
<configuration xmlns:patch="http://www.sitecore.net/xmlconfig/">
<sitecore>
<processors>
<uiDragItemTo>
<processor patch:before="processor[@type='Sitecore.Shell.Framework.Pipelines.DragItemTo,Sitecore.Kernel']"
type="YourNamespace.Draggable,YourAssemblyName" method="IsDraggable"/>
</uiDragItemTo>
</processors>
</sitecore>
</configuration>
My recommendation is to go for Solution 2.