Nope, because power plants have generators that output AC (pretty much always 3-phase). Not to mention every generator you can buy in a hardware store has AC output (usually single-phase).
A generator is a device that converts mechanical power into electric power. A dynamo is a generator that uses a commutator to produce pulsed DC. An alternator is a generator that produces AC (which may later be rectified & filtered to DC). The term "alternator" is usually restricted to small generators used in automotive applications, larger AC generators such as those in power plants get described more precisely, e.g. induction generators or self-excitation generators. There are some other less-common generator types, such as homopolar generators that output continuous DC.
Interesting, in cars the terms "generator" and "alternator" are used to refer to a DC device (dynamo?) and an AC device, respectively. Cars used DC generators for their electricity until the 60s/early 70s (depending on make/model) when they started using an AC alternator with a rectifier to make a constant 14VDC.
Not enough dynamos: build more dynamos.