If the concern you have is over the puffer's toxin then no, the dead one's tankmate will not be poisoned for two reasons
1) they are immune to their own toxins
2) they are most likely captive bred and therefore are unlikely to have any toxins anyway as they get their poison from the diet they eat in the wild.
I don't know if my DPs were wild caught or not, but when they died I had to get them out ASAP or the other fish in the tank (kuhli and black kuhli loaches) would try to eat the body and would die. I never had an instance of a puffer dying from eating another puffer though. Either they didn't like the taste or they were immune to the poison. My dwarfs always prefered live foods anyway. SirMinion's response suffices though