I'm going to be blunt here, I think having, or not having, a sink in the island is not the main worry here. I echo what PPs said re the oven.
In the first shot, the area looks huge, the island looks like it belongs. However, when you see the reverse angle in the second shot, the island looks like an obstacle with a lot of wasted space at the far wall.
If a kitchen planner drew up this plan for me, I would be looking for a better kitchen planner. I walked away from one kitchen planner who clearly had never cooked or washed up in his life and I found a better one for me.
If this was my kitchen, I'd be looking at building a j--shape or u-shape against the back wall, scrapping the island completely and maybe having a peninsula at the end of the run of wall units to accommodate some kitchen stools - leaving yourself plenty of room by the patio doors for a substantial table and chairs. When you have guests you can throw the doors open and have an indoor table and an outdoor one too.
Admittedly, this is me with a 4 person family who sit and eat as a family once, twice or thrice daily - rarely entertaining at home - and when I do, the cooking is not a performance, but the food is good.
I think islands are a trend that may be coming to the end of their trendy lifespan anyway. You are looking at a huge investment here, I'd spend some time looking on Pinterest at some kitchen/diners or pop to your local newsagent for a specialist magazine or two.
Or, perhaps you intend having a table and chairs at the wall end? Not sure why your run of units end at that end of the kitchen, perhaps there are doors to a living room at that end that we don't see?