No, flightaware doesn’t even show the exact position on your local map unless you change a dump1090-fa setting.
On the webpage you can’t even make it display an exact position, it’s always rounded.
You can chose to round to full degrees even.
From the stats page where you also configure you location:
Precision on Coverage Map ( )Exact ( )1 km ( ) 10 km
(exact didn’t work last time i checked bu it’s not what you want anyway)
Just open your own stats page in incognito/privat browsing mode and you should see what others see.
You are lucky that your MLAT is even working 
Anyway set it to 10km if you are concerned about it.