Measure RF impedance of PCB or IC using a VNA Network Analyzer
I'll answer the parts of your question where I understand what you're asking:


  Can I use a VNA to measure the impedance of the MCU?


If the MCU is powered on and transmitting, it could produce spurious readings from the VNA.

If the MCU is shut down, it will likely not have the same equivalent impedance as when it is operating.

If it can be turned on and put in a no-transmission mode, you might be able to get a good measurement.


  Am I going to break my VNA if I plug a constant TX device into it?


Not if the output power is below the maximum input level for the VNA. 

But again, the signal coming from the TX could cause erroneous readings.


  I currently don't have the calibration tool and it costs $6K... For this exercise what is the consequence of no calibration? Can I make my own coarse calibrator?


There are alternate cal kit vendors, but I doubt you'll find a decent kit for under $1000.

You could try measuring some known devices to see how accurate your VNA is without calibration.

It'd be unlikely you could get a good measurement of the \$S_{11}\$ of a well-matched load without calibration (but you could probably verify the load is not totally broken and behaving like an open or short).