No, the nuke is originally set to launch by Makarov or the Russian military. Task Force 141 infiltrates the sub station to prevent this happening, but Price goes rogue and launches it anyway - apparently setting it to detonate in orbit, however. His reasons for doing this are ambiguous (he says that, "The only way to put out a fire is with a bigger fire"), but I'd speculate it was to disrupt fighting on the ground in the States and/or divert military attention elsewhere.
