Yeah, no.
Just do a bit of undergrad Aero math. Each Tungsten "telephone pole" would have to weigh 24,000 lb each. They say they would have to be made out of Tungsten so they can make it through the atmosphere from space at Mach 10 + and not burn up.
- It's technically and financially prohibitive to send that heavy of payload into space. Easily researched, the cost per pound to send payloads into space is $10,000 per lb. So even if we say we have 10 rounds up there, the cost would be 10,000 x 10 x 24,000 = $2.4B. If you think we sent 100 rounds, that's $24B. Not happening. Especially with no one knowing.
- Aerodynamic heating goes up with Mach^2. So, conservatively from basic Compressible Aerodynamics, Mach 10 would raise the static temp up by a factor of 700. A very low upper atmosphere temp is 100 Kelvin (K). Initial temps for the Rod from God to encounter is 70,000K. Melting point of Tungsten is 3695K.
Copy it could slow down like the Shuttle and get through but then the super kinetic weapon factor goes away. The Shuttle slowed quickly and continued to slow, subsonic in most of the real atmosphere, landed at 225 Kt, Mach 0.3ish.
Even Mach 5 is really fast and hot in the normal atmosphere. Hotter than 3695K.
Edited: for bad undergrad Aero math on the cost to space. Maybe...