aye, in fact I think it's possible to prove that it works with any configuration of black and white such that no two black squares touch.
if the tank starts on a black square, you must bomb all black squares and then all white squares. If the tank starts in a white square, you must bomb all white squares and then all black squares and then all white squares. Therefore the bombing run must be W-B-W.
Therefore the total number of bombings must equal nW*2 + nB to destroy the tank, where nW + nB = 1681 and no black squares touch. Thus the problem is finding a configuration of black and white such that no black squares touch and nW is as low as possible. The obvious answer is the checkerboard which makes nW = 840 and nB = 841.
this doesn't actually require that all the white or black squares are bombed at the same time. So long as any possible sequence of tank motion(ie a square + all its neighbors) are bombed in this pattern it will work, it's just easier to determine the pattern beforehand and do them all at once instead of iteratively. For instance, bombing on successive diagonal stripes across the board(I hope this image gets across. Like starting in the top-left corner, then bombing its neighbors, then bombing the top-left corner again, then bombing another diagonal stripe) is actually the same as the checker board, just in a different order. I hope that made sense.