Can systemic intravascular thrombosis cause brain infarction?
No, a thrombus would be much too large to pass through the highly selective blood brain barrier.  However, there are some cases where intra-vascular thrombosis can cause stroke.  

One example would be non anti-coagulated atrial fibrillation, where the inefficient beating of the heart causes blood to remain stagnant in the left atrium.  This can cause a thrombus to form within the atrium which can then throw off emboli, some of which may enter the cerebral circulation. These may then partially or fully occlude one of the arteries in the Circle of Willis (the brain's circulation system), however the blockage is proximal to the blood brain barrier.  

See Management of atrial fibrillation (GY Lip,2007) or for those hitting a pay-wall the professional reference section on AF