This whole concept breaks at the $^2$ of $E = {1 \over 2} m v^2$.
You must realize what speeds are involved, and what energies appear as result.
1kg of TNT has a little over 4 megajoules of energy - as chemical energy of its explosion.
1kg of pretty damn much any material in Low Earth orbit has 32 megajoules of energy.
That means a kilogram block of, say, wood, hitting a thick surface at LEO's 8km/s will cause a crash that will behave as an explosion 8 times stronger than a kilogram of TNT detonated at rest on that surface.
So, picking payloads like that, dropping them off, and using the raw kinetic energy of the train in that process just won't work. You park your payload in LEO (traveling at 8km/s), then the train arrives at 11.3km/s from Mars, and tries to grab the payload, with 3.3km/s speed difference. 3.3km/s speed difference is 6 megajoules/kg. Instead of grab-and-accelerate you have a crash of energy equivalent of roughly 1.5 times the payload weight in TNT. Nothing will survive that.
What you CAN do though, is to launch a nice, comfortable ship with life support systems, artificial gravity, plenty of storage space, good shielding, generally a comfy long-term 'space hotel.' Put it in the cyclic orbit. Then, when it comes, launch a supply ship - just a dumb tube stuffed to the brim with food and necessities; and a passenger capsule - a small, rugged, cramped thing that has enough oxygen and food for a couple days - then using the rocket engines match trajectory, dock them to the cycler, and board it. Use the supplies, facilities, have the crew live in relative comfort on the way to Mars, and then have them board a reentry vehicle, another rugged capsule, that will be able to land on Mars. Cycler goes back to Earth, the capsule brakes against Mars atmosphere and lands at a base. Possibly a different crew launches in an ascent vehicle to board the cycler on the way back to Earth.
The cycler would never enter orbit of Mars or Earth - it would only do fly-bys. It would hardly accelerate or decelerate. It would just serve as a comfortable mobile base. No energy savings on accelerating/decelerating the payload, but instead of a cramped capsule to Mars, you get a space hotel to Mars.