I see some things that will make this pretty close to impossible. In the one little part where you drew the white Polylines over the grey Blocks:

most of the Blocks are duplicated, almost but not quite in the same place. This selection is two Blocks on top of each other:

[and note that the Polylines don't meet], but their insertion points are not the same, and neither one is on the line:

And I found at least one place where the series of Blocks in a straight row, presumably to be drawn over with one line, has a reversal of rotation midway, a point where two Blocks are inserted at the same place but have opposite rotations, and there are two rows of Block progressing in opposite directions from there.
Even with such peculiarities corrected, it looks like a staggeringly complex task, to get a routine to be able to detect which Blocks belong together in sets, with the same rotation, and collinear insertion points, and presumably some kind of adjacency or spacing test, made more difficult by the varying scale factors. And they're not always in drawn order in a given row, either, so determining the extent within a set [which two Blocks are the ends of the row?] would be another challenge. Even after figuring that out, there's the further complication that each Line would need to extend not just between the endmost insertion points in a row, but at one end through the width of the last Block to the far side midpoint [a different distance as the scale factors vary]. That is sometimes the location of an end of a Line over a different row of Blocks, but it might be the through-to-the-other-side midpoint for both rows, i.e. with no insertion point at all there. If they should be Polylines, determining which sets meet in the right way at which ends is another problem -- it would probably be better to do Lines, and join those that can be joined after the fact.
With only MIDpoint Object Snap running, you could draw a powerful lot of these Lines/Polylines in the time it would take to work out a routine to automate the process, if that's even really possible. [In your original drawing, MIDpoint alone wouldn't do for one of the Block types, because it would latch onto an off-center location relative to the overall Block, but ENDpoint or INTersection would be needed.]
Kent Cooper, AIA