The "exhaust grill" we often (but not always) see is, in my opinion, a heat exchanger more than a thruster, and not all ship's even need that much external hardware for the impulse engine to run.
In support of this, the impulse engines typically glow even when there is no propulsion taking place. And if they glow more intensely on occasion, it's not in correlation with propulsion taking place - at most, it's in correlation with an exceptional amount of propulsion taking place (mainly in TOS-R), which might involve things overheating and this radiator glowing to get rid of the waste heat.
Since the "nozzles" are seldom situated anywhere near a plausible thrust axis anyway, exhaust-based thrust is unlikely from the very start. However, this doesn't mean there couldn't be some exhaust vectoring in addition to the main propulsive action - rather comparable to some aircraft piston engines deriving (marginal) extra thrust from angling their exhaust pipes aft! Indeed, some ship designs feature what looks like mechanical thrust reversers (see the E-E nozzle "lips") even though their "nozzles" are angled in funny directions to begin with and are rather unlikely to spit flames directly aft.