Good question. USS Langley, the first aircraft carrier the US built and commissioned had electric drive. This was a conversion from a 1910s electric drive collier. At that time reduction gear drives were not yet mature enough and the USN experimented both with electric and geared drives. Simultaneously, in the 1910s, the US built 6 battleships with electric drives (turbo-electric propulsion). The USN seemed rather satisfied with the arrangement, and proceeded to build 2 fleet carriers (45,000t) with electric drive. It had plans to build six largest ever battleships at the time (48,000t) in 1920, also with turbo-electric propulsion. However, the Washington Naval Treaty smashed those plans.
The main argument against turbo-electric propulsion that I could find cited is excessive weight. Nonetheless, the US launched roughly 120 destroyers with turbo-electric propulsion in just 2 years (1943-1944).
No, such arrangement doesn't have to be IEPS.