We study the effect of secondary structure formation on cooperativity of protein collapse using a simple homopolymer model on a "210" lattice that allows a geometrically consistent representation of alpha-helical conformation. Monte carlo simulations were carried out in the range of temperatures and energetic parameters that characterize relative strength of global (i.e., between monomers that are far apart in sequence) and local (helix-stabilizing) contacts R = eta(g)/eta(1). The complete phase diagram presented here exhibits a narrow region of temperatures and R-values in which compact conformations with considerable helical content dominate the equilibrium. It was shown that at certain values of R, the collapse transition occurs in a narrow temperature range and is accompanied by a pronounced increase of helical content. However, the simulations do not support a two-state transition scenario at which transition occurs between two (metha) stable states corresponding to free energy minima. Rather, we observe at all temperatures and all values of R a single stable state that evolves, as temperature gets lower, toward more compact conformations. We argue that additional factors such as sequence specificity and/or side-chain packing should be taken into account to explain the two-state character of folding transition observed in real proteins.