I have found 2 tarps on my allotments so far though with wood chip on and lots and lots of weeds! Not sure if they came up or seeded onto the wood chip, but its the devil to get up. I think the problem may be that whoever put it down, left it and didnt weed at all.
It's true that weeds will eventually open those tiny holes into bigger ones (especially the underground couch) but the maintenance is so much easier and quicker than bare soil.
Woodchip gives you about 1 - 2 years before it becomes a growing medium in its own right - but at that point it becomes very valuable as a soil conditioner (you can basically see when the nitrogen robbery has stopped and the weeds start to enjoy it).
At 2-3 years it's brilliant on its own as a really light medium for pots and containers - especially for plants that aren't greedy and don't really like heavy soil - carrots are the obvious example - they taste better in heavy clay soil (more trace elements?) but they don't like pushing through it, so a thick layer of rotted 2-3year woodchip gets them going and the clay waits below with its extra nutrients.
I like to go one step further by using builders bags for cloddy weeds to about half full, then putting weedy rotted woodchip on top to 3/4, then topping up with at least 15-20cm of clean 3 year woodchip for sowing carrots well above the carrot fly. I also put taller plants along the N edge - almost everything seems to grow to twice the size it is in clay.
NB. you do need to hose it well as you build it - especially to soak the strawy stuff - but then you get a population explosion of slugs & snails, so you need pellets as soon as you top off and sow - or they just razor everything off. I am experimenting with keeping 90% of the pellets in 500ml bottles (thanks to Digeroo) just in case the (invisible) hedgehogs can climb that high.