I forget the percentages, but I did read somewhere that the road surface accounts for a far larger percentage of your total grip than the choice of tyre does. Of course this isnt the same me saying 'I recommend you just fit cheap ditchfinder tyres, then' - the better tyres still increases grip of course, but compare your grip levels on Pingpong XL crossplys on hot, dry tarmac, vs Goodyear Eagles on wet, oily uneven roads as you'll take my point.
Anyway, point being, that yes, the road surface affect grip in a large way. However that's surely in cornering, however, in a straight line I'm not so sure what affect that will have... negligable, or less? Unless you're actually wheelspinning when you set of, and a grippier surface would let the wheels literally grip quicker, as I say, not sure that the road surface isn't only a tiny amount.
Also I'm well aware that I have used the 'I did read somewhere' line, so please take my opinion with the same pinch of salt that you would with the bloke in the pub who has a mate who knows a guy that definitely knows about cars