4th dimension, warning time? Is there any,

Speed is relative, so our velocity compared to galactic stationary doesn't matter much.

However, if its coming straight at us in 3-space at 99% of the speed of light, the amount of warning is related to both how far away it was to start with and how close to the speed of light its going relative to us.

If its a stray brane drifting at us along directions other than the usual three, then I'm not sure how there could be a warning. Just, bang.