Stumbled over the idea on one of the older minecarting threads and it only makes sense, so i tried it out and it works as expected:
instant signal propagation via minecart. Ramps can only accelerate carts to ~2,7 tiles per step, collisions some more. But arbitrarily slow carts can propagate a pulse instantly over any distance. You just need enough carts:
I-MMMMMMMMMMMMMMMMMMMMO
"input" cart I hits a long unbroken line of "M"inecarts, "output" cart O starts moving the moment "I" collides with the first cart in line.
Two points, however:
1. you need to "prime" the cart-tube with a first collision; on that first go, the pulse will propagate at seemingly twice the movement speed of the starter cart
2. every cart in the line must be _older_ than the one it pushes.
ad 1. sub-coordinate matters: a cart placed by a hauler dwarf starts out in the middle of the tile. It will only check for collisions when it leaves its current tile and will only leave once its sub-coordinates put it past the "tile border". If it collides and stops, it will do so exactly on the border. Getting from the middle of the tile to the end takes ~half the time crossing a tile from end to end would take, hitting the border when already on top of it is practically instantaneous. The sub-coordinate only matters when pushing, though, not when getting pushed; a line of carts all sitting on the border generally get pushed, start moving, collide and push the next cart, all in the single sub-step during which they calculate their movement.
ad 2. Minecarts take their turns during movement resolution by build order, oldest carts first: oldest cart tries to cross tile border, collides with second oldest, pushes it and stops (still on the border); turn resolution now passes to the next oldest cart, which, just having received a pulse, tries to cross the border, pushes the third oldest cart, stops on the border and turn resolution carries on with the third oldest cart. This way, with a perfectly-ordered line of carts that's already primed, the pulse goes through the entire line _in a single game step_. I made sure that the last cart is also on the very border of its tile and could "tunnel" a dwarven push through seventeen carts in a single step - the last cart started moving on the very step that the input cart smacked into the first in line. Longer lines are possible, but the practical use is nil.
2a. weight of carts should go down or stay completely constant along the line; lighter carts pushing heavier carts result in a reduction of speed, and heavier carts pushing lighter (standing) carts don't have the opposite effects; discrepancies in cart weight lead to speed loss.