Alloying metals with other elements is often done to improve the material strength or hardness. A key microscopic mechanism is precipitation hardening, where precipitates impede dislocation motion, but the role of such obstacles in determining the nature of collective dislocation dynamics remains to be understood. Here, three-dimensional discrete dislocation dynamics simulations of fcc single crystals are performed with fully coherent spherical precipitates from zero precipitate density up to p(p) = 10(21) m(-3) and at various dislocation-precipitate interaction strengths. When the dislocation-precipitate interactions do not play a major role, the yielding is qualitatively the same as for pure crystals, i.e., dominated by "dislocation jamming," resulting in glassy dislocation dynamics exhibiting critical features at any stress value. We demonstrate that increasing the precipitate density and/or the dislocation-precipitate interaction strength creates a true yield or dislocation assembly depinning transition, with a critical yield stress. This is clearly visible in the statistics of dislocation avalanches observed when quasistatically ramping up the external stress, and it is also manifested in the response of the system to constant applied stresses. The scaling of the yielding with precipitates is discussed in terms of the relation.