Simply, No. [How does one get red pen in this formatting box?] At a given constant velocity a vehicle will require the same force to overcome drag and frictional losses on a flat road regardless of the mass. If you wish to change the velocity then mass will become relevant, or if the vehicle is travelling up or down an incline.
But I'm definitely sounding like a sad **** here so I'll leave it there. I think we all know that the different ride height of a GTV with a full tank or a GTV with an empty one will have minimal effect on v-max, but the extra mass will have a more significant effect on acceleration. I know the one with a full tank will travel further though. Now for an F1 car the different ride height of a full/empty tank does matter for aerodynamics enough to determine lap times ...
I did once read someone suggesting that extra weight over the wheels helped make their car handle like it was on rails
. I think could be the USA school of handling from the 1970s.
I also read once on a VW forum that after an ECU remap their car was only doing 4k rpm at 80mph, whereas previously it had needed 4,500rpm in top gear for the same speed.
Bless the ignorant, but don't let them suffer.