The satellites only provide single coverage i would expect. For MLAT you need the area to be covered by 4 satellites which would be well a lot more expensive.
It’s a service for companies who pay, and companies who pay will equip their aircraft to transmit locations.
Most airplanes companies want to track come with ADSB anyway due to new regulations.
Anyway you can check on your signal strength with this file:
http://IP_OF_YOUR_PI/dump1090-fa/data/stats.json
Just post the last block starting after local.
Or you can just check for signal / noise, which is given as dB full scale.
Then there is the number of accepted messages and strong signals.
The percentage of strong signals gives you a good hint if you should decresase or increase gain.
If your antenna is suboptimal though most likely the default setting is fine.
Anyway you should consider building a so called quick spider
(QUICK SPIDER - No Soldering, No Connector)
from some coax that comes terminated with an SMA connector, something like this:
(https://www.amazon.co.uk/d/Antenna-Cables/Antenna-Extension-Coaxial-Wireless-External-Gold/B073TXBS7V/ref=sr_1_4?ie=UTF8&qid=1546984004&sr=8-4&keywords=sma+cable)
Or just get yourself this ebay antenna from hong kong:
(https://www.ebay.de/itm/1pcs-ADS-B-PCB-Antenna-1090MHz-Antenna-SMA-female-Antenne-CASE/253915016420)
That needs not only a cable but also a male to male SMA adapter.
Enough rambling have fun with your ground plane 