No, there does not need to be visible plasma, and smoke alone is enough to constitute a fire onboard an aircraft.
FAA Advisory Circular 120-80A contains the following definitions that indicate that a visible flame is not the only definition meaning "fire" pertaining to aircraft. In my experience, it's reasonable to expect that the FAA's definitions in this case would fall in line with the NTSB's definitions.
Fires that are “hidden” are not readily accessible, may be difficult
to locate, and are more challenging to extinguish. Some examples of
hidden fires would be fires behind sidewall paneling or in overhead
Combustion without a visible flame and a slow combustion rate are
characteristics of a smoldering fire. A smoldering fire left
unattended or an incompletely extinguished fire can ignite and grow
into a larger, uncontrollable fire in a short time.
A fire that has been partially extinguished which may or may not have
visible flames. A suppressed fire, if not extinguished, may
reestablish itself and grow into a larger, uncontrollable fire in a
short period of time.