That looks dangerous to me. I'd be scared someone at the sink would forget it was open, step back and fall right across that open door.

Straightn out whtever jog is to the right of the sink and put it there. Straighten out the other bumpouts as well. They diminish utility and add expense.

In a word, No. You can put a DW there, but it is not functional, not safe and the more you use it, the more you will hate it. If you sell your house, there are a lot of things a buyer may overlook about a kitchen, but they will notice cooktop/double ovens or range, sink and DW. In most cases, folks want to make sure the kitchen has a DW and maybe how nice it is vs how soon they would be replacing, but ini your case it would likely be a no sale or only at a price that merit gutting the kitchen since the cabinets would all have to be reworked or replaced.

Sorry, but I think the advise to straighten out your jigs and jags would be well taken.

How were you planning on running the dishwasher drain? Wrapping back around the wall to reach the sink plumbing looks like about 8'.

My DW is on an adjacent leg of my U kitchen from the sink, and we don't mind it (in fact, we did it again when we remodeled). But this configuration looks dangerous, as others have said.

OP, what's the thinking behind the shallow cabinets around the sink? I would have permanent bruises on my hips if I lived there. It looks like you're trying to center the sink on the window. While I appreciate that desire (assuming that's the reason), it throws off the function way too much, not only with the odd corners, but reducing cabinet and counter space.

Where are your range and fridge? Perhaps if you posted a layout, we could help you rearrange things.

I have a very similar set up in my current kitchen and I absolutely hate it. When I am at the sink and loading the dw I get trapped in there. If someone is at the sink getting a drink and someone else needs to get to the sink, or the dw, or the garbage, they have to wait their turn. I would not do that.

I like having my dishwasher right new to the sink, so that when you rinse a dish you carry right over the counter to the dishwasher. My floor would be sopping wet in that configuration. Maybe others are neater than I am!