So I was testing various levels of tyre wear the other day and thought I could part test your question whilst I was at it. In short, I setup a private lobby at ran sets of 10 laps at Brands GP. At the end of each 10 laps, I pitted for fresh tyres and didn't top the fuel up. On my first set of 10 laps, I actually posted my fastest time on my 9th lap, I put this down to requiring a few laps to get my eye in with the particular car I was driving. On lap 12, my first hot lap on hot tyres, I beat my previous best by 0.300. Fresh tyres and no fuel on lap 20 and by lap 22 I beat my previous best by 0.500. Unfortunately I stuffed it on lap 32 (the pressure got to me), I was 0.250 up at the second time split but had already lost it off the left-hander where you leave the Indy circuit. Throughout my testing, I was regularly able to make up time on the GP section of the track, to lose it all on the Indy section, where downforce wasn't able to compensate for degraded tyres.
Conjecture leads me to believe that if you had the patience, then yes, you could run faster times with tyre/fuel depletion turned on, as you might perhaps expect 👍
{Cy}