I think you are asking two questions:
- Can tweed be used for a DB?
- Can you wear a tweed DB w/o a tie?
I think for (1) there is historical precedence and the example you show seems no more radical than a slubby linen or wool DB so why not. For (2) any jacket can be work w/o a tie BUT should you? Since the traditional shirt for a tweed w/o a tie is a OCBD you would be wearing a BD with a DB. Again - certainly possible but it would violate a basic rule.
Finally - the jacket looks slightly feminine - the combination of the shape and colour (or flash?) combined with 4 button stance. Nothing wrong with that if you are comfortable with it.