The answer, with no more info than what is given, is 'yes.'
Cars have lubrication and cooling systems to prevent overheating, for a reason.
You really cooked that oil.
My wife is an office manager for a collision and service shop that serves a wide variety of cars: from Teslas, to Jags (vintage and new), BMW, Cadillacs, Mercedes, Lexus, Rovers as well as all manner of 'normal' cars. Heck, they even serviced a Batmobile replica.
Just yesterday she was telling me that they had three different cars in the shop right now awaiting new engines because owners had run their cars overheated.
Have owned, enjoyed, appreciated, and now all gone:
1969 Europa S2 Blue
1970 Europa S2 White (my first)
1974 Europa Twin Cam Special Light Blue
1974 Europa Twin Cam Special #4380R Indigo Blue (my absolute favorite).
1984 Turbo Esprit Calypso Red
2005 Elise Starlight Black
2005 Elise Saffron Yellow
2005 Elise Ardent Red (used as development mule for the LETSLA)
2006 Exige Graphite Grey
2007 Exige S Canyon Red (first customer installation for the production LETSLA)