If we were to model a universe without any dark matter in it, would stars and other large scale cosmic structures (galaxies or clusters) form in timescales similar to our universe? Or would they never form at all?
The answer is, it depends. If you take the usual $\Lambda$CDM model and then remove the cold dark matter, then no, you wouldn't get the same universe at all. In fact the dark energy would dominate the energy density of the universe at an earlier time and the structures - galaxies, clusters of galaxies - we see in the universe today may not be able to form from the primordial fluctuations that we see evidence for in the cosmic microwave background. In fact those fluctuations are primarily due to dark matter (in the $\Lambda$CDM model) so the growth of structure would be starting from an even lower base.
The key question is I suppose do things like galaxies etc. form at all, or do they just take longer to form? My understanding is that in order to grow into the galaxies, clusters and superclusters that we see today, without dark matter, then the CMB fluctuations would need to be more like 1 part in a 1000, rather than the 1 part in 100,000 that are observed - and this is without considering dark energy, which will act to make structure formation more difficult.
The reason I started the answer with "it depends", is that there are alternatives to $\Lambda$CDM, namely the modified gravity theories such as MOND, MOG and TeVeS, which do away with the idea of dark matter and modify General Relativity at large scales and small accelerations. The most vanilla versions of these theories fail to explain structure formation in a satisfactory way, especially at large scales (e.g. Starkman 2011) but more complex versions are possibly still competitive (e.g.Dodelson & Liguori 2006)) - I will leave others to comment on that.