I feel it depends on the plant's growth habit, the climate/environment, the type of compost, as well as the depth of the compost and chips (like others have said).
I tried last year to grow some brassicas in a layer of composted rabbit manure on top of wood chips and didn't have good results. Since the root systems of the things I planted are typically shallow, they basically kept the roots above the chip layer and dried out quickly, and never accessed the nutrients/minerals in the soil under the chips. Additionally, it seemed like every grass/weed seed that blew in and landed on the compost germinated & thrived. In an attempt to retain moisture and suppress weeds I tried adding another layer of chips to the surface, and found it was very difficult to dig through the 3 layers (which hadn't broken down much) this year. Oddly, though, the volunteer brassicas and the seeds I broadcasted over the chips seemed to do fine with sprouting in the chips and sending roots down to the soil.
With that said, I have also added compost to the chips and used a rake to mix the compost with the wood chips on the surface and planted seeds/transplants in the mix. Stuff like squash/melons, tomatoes, corn, and other rapid growers did fine with it; I assume because the roots were quickly able to reach the soil. Beans, peas and peppers were a little slower, but eventually took off.
Things planted before it got really hot and dry did much better than the things I planted later in the spring/summer.
You may end up with totally different results in your climate than I did in mine, so my thought is to try different things and see what does best. Let us know how it turns out!
