Do female turkeys reproduce without a mate?

No. Turkeys cannot asexually reproduce. The reproduction of turkeys requires two parents, therefore they can only reproduce sexually.

Edit:

Examples in animalsA number of invertebrates and some less advanced vertebrates are known to alternate between sexual and asexual reproduction, or be exclusively asexual. Alternation is observed in a few types of insects, such as aphids (which will, under favourable conditions, produce eggs that have not gone through meiOSis, essentially cloning themselves) and the cape bee Apis mellifera capensis (which can reproduce asexually through a process called thelytoky). A few species of amphibians and reptiles have the same ability (see parthenogenesis for concrete examples). A very unusual case among more advanced vertebrates is the female turkey's ability to produce fertile eggs in the absence of a male. The eggs result in often sickly, and nearly always male turkeys. This behaviour can interfere with the incubation of eggs in turkey farming.