My gut instinct is that muscle would be more vascularized than fat. Even if it isn't, the function of fat is to store energy, while the function of muscle requires using energy, and also requires more oxygen supply to support the use of that energy, so if someone has gained a lot of lean muscle mass while losing fat, without adjusting their nutrient intake, I would think it's possible to develop anemia...especially if their iron intake was just borderline sufficient in the first place (if they had been consuming excess already, it might not matter).
It is vascularized. During exercise, the blood flow gets shifted. Blood flow goes to the skin to vent off excess heat. It goes to the working muscles and heart. Blood flow tends to really drop for other part of the body like the gut and so on. Fat like the gut, would take up some but very, very little.
Fat is pretty vascular, not as much as muscle, but still there. As mentioned above there is some shunting with exercise, but that mostly is from the internal organs. As you warm up, there will be increased blood supply to the skin, which is lined by fat, so there really is not a tremendous amount of shunting from fat. Depending on how deep the fat is, it can be quite vascular. I have seen some tremendous size vessels supplying the fat stores of some big folks.
If it weren't vascularized, it would die. But, being mostly inactive and not requiring lots of oxygen, it's minimal, thus allowing procedures like liposuction to be relatively safe.
I agree that fat has some vascularization, but disagree with conveying that liposuction is relatively safe. Liposuction is extremely risky in the short and long-term, (for so many reasons), and from my understanding, liposuction doesn't make biological sense.