planetary formation - Can protoplanetary disks form main-sequence stars?

No, not really.

Stars can form in circumstellar disks, that are, in general, disks surrounding forming stars, but not in protoplanetary disks. Protoplanetary disks are, by definition, flat, rotationing disks composed of gas and dust, found around newly born low-mass stars (see the review by Williams & Cieza (2011)). There are two important point in this definition: protoplanetary disks orbit around low-mass stars, and, in particular, newly-born low-mass stars. These two points are important, because at this stage of the life of the disk and for this range of stellar mass, its mass it clearly too small to form any star.

That being said, it is not impossible to form stars in the protostellar disk of a forming star (that is one of the possibility to form multiple systems, that are still hard to explain), as discussed by various authors (see, for example Stamatellos et al. (2009), Vorobyov et al. (2013), Joos et al. (2013) and many others), but it is more likely to form brown dwarfs of very low-mass stars in these disks than main sequence stars (their mass is simply too small, once again).

That being said (bis repetita), you could, as pointed out by called2voyage, you could form a main sequence star in the circumstellar disk of a high-mass star (as a Wolf-Rayet type star).