I highly doubt it, as the rotation of the tire wil fling most of it off once you are moving at any appreciable speed. However, there is a reason they commonly call diesel fuel in the old days "diesel oil." A bigger concern to me would be potential contamination of the brake pads and a potential temporary reduced traction if some got on the tread.

But I'm not really concerned about it... it looks to me like it would be difficult to get it on the brakes, and any on the tire would be temporary. Next time you wash the car, turn the hose onto the filler door and see how much gets onto the tire and brakes... not much I'll bet.