Dear James,
Sorry for the delay -- I hope you're still in the rainy season and my response is not too late to help! 
Topdressing is simply adding sand. The effect of the sand depends on grain size and uniformity. If the grains are small and uniform, sand is better than grass! Try Daytona Beach Florida sometime: It stimps 15 and is as true as marble. But if the grains are largish or not especially uniform, the sand wreaks havoc with the direction of the roll and causes variation offline, especially at the end of the putt when the roll slows.
Topdressing also has an effect on distance control, as non-uniform sand particles tend to make the surface slow. Even worse is when there is moisture on the sand. Then the sand clings to the ball and really messes up the roll and slows down the ball. As topdressing and watering go together, this clinging sand is a major problem.
You don't mention aeration holes, but topdressing and aeration often go together, so let me address that also.
Basically, aeration holes in the green are uniform in size and spacing and present little disc-shaped areas where the surface is lower than the rest of the green, with sand not quite topping the hole off at the right level. Typically, from aeration to recovery takes about three weeks or more, with intermittent spreading of sand to fill the holes and with only sparse mowing to let the grass recover and grow back into and over the sand-filled holes. So an aerated green is a bit like a peg board.
Putting across a peg board affects the speed and the direction of the putts. A rough surface presents more opposition to the ball than usual and hence takes energy out of the putt. So aerated greens have to be treated as especially slow greens.
Putting across the grid-like pattern of the holes also has an effect upon the line or path of the putt. It's a bit like Pachinko, with the ball ricocheting off the holes back and forth as it crosses the surface. But the aeration holes don't protrude from the surface like bumps or Pachinko pegs, but are recessed little bowls the ball falls into and hits the far side edge and then goes off any which way from one hole to the next. But overall, the grid-like pattern of aeration holes results in putts having less break, and balls started off in direction X don't stay headed that way very often but go offline plus or minus a fairly predictable range of degrees. Big aeration holes cause more off line rolls than small, and dispersed grid patterns cause more off line than tightly spaced holes in a grid. Deep holes cause more problems than sand-leveled holes. Putting uphill into aeration os more disruptive than putting downhill, sort of like grain.
Basically, it's a crap shoot, so enjoy your day and don't expect much.
Cheers!
Geoff Mangum
Putting Coach and Theorist
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