I was under the impression (perhaps incorrectly) that the in-camera
metering effected the output of the camera's light meter and in no way
effected the actual exposure when the shutter is pressed (in manual
mode). Is that true?
True, as far as it goes, but...
And I thought it was a good question that all photographers really need to understand.
In camera A or P or S mode, the light meter changes the exposure settings, f/stop and/or shutter speed settings, for a correct exposure.
In camera M mode, it does NOT change the settings. What you said, Manual is Manual.
The light meter does still read and show the exposure, it just does not change the manual settings to match it.
However, any TTL flash power level is still automatically adjusted by the light meter, even in camera M mode. Camera metering modes are about Ambient. TTL flash works into any ambient settings it finds are present when it is triggered. We can also set Manual flash level if desired.
This has two possibilities then, camera in Manual mode.
You can manually "zero" the meter to 0 EV (including the meter seen in the viewfinder), meaning by actually changing the settings until the light meter reads zero, and this will apply that same exposure change, same result as if the lightmeter did it. This is what many users mean when they say they always use Manual exposure. It is just using the same meter reading in a different way, a difference in WHO adjusts the same settings. However, it does offer easy opportunity of leaving it a third or half stop off, as compensation.
If Auto ISO is ON, Auto ISO will still work in Manual mode. Meaning, the Auto ISO adjusted result will likely give you a correct exposure, using the unchanged f/stop and shutter speed, at maybe ISO 2500 if necessary.
Some users use Manual that second way, as an automatically adjusted exposure. They might set say f/5.6 1/800 second (I am making up numbers), the user thinking those specific values are more important than ISO. And then this lets Auto ISO adjust to give the automatic correct exposure at those manual settings (works within the range of Auto ISO). Manual settings, but Not manual exposure.
For a long time I have considered getting a high quality hand-held
light meter but most pros don't seem to need or use them so it seems
like just one more piece of gear to haul around.
The main advantage of a hand held light meter is that it can be an Incident meter, which reads the actual light directly (that light actually incident on the subject). This is as opposed to a reflective meter (like necessarily in cameras), which read the light reflected by the subject.
This incident meter may be awkward outside in the world, since it is metered at the subject (in the subjects light) instead of from the camera. However, Incident is wonderful in the studio, because it will meter the flash, and the subject location is handily available, and the lighting does not change during the session. Lighting can be set up before the subject arrives, subject is unnecessary for metering, only the light at their location matters. So one metering of each flash sets that flash power level, and sets a lighting ratio, is good for the entire session, and is easily duplicated next time too. (Exception: a hair light really has to be adjusted by eye, on the subject).
Reflected meters are aimed from camera towards the subject.
Incident meters are aimed from the subject towards the camera (Not affected by subjects reflected colors).
Incident metering is significant because...
A white dress reflects a lot of light, and the reflected meter will read high, and therefor the reflected light meter system will drop exposure of it back to middle gray.
A black dress will reflect little light, and the reflected meter will read low, and therefore the reflected light meter system will boost it up to be middle gray.
A Spot meter is simply a reflected meter, so we better know and consider something about the reflectivity of that spot. :)
FWIW, haze reflects light too, seen by the reflected meter. Haze blocks the light seen by an incident meter.
Reflective metering of all subjects seeks a middle gray goal (meaning overall average of the metered area seen). That exposure may not be correct unless the subject reflects an average mix of reflectivities, actually averaging about middle gray to match the meter. I do not technically mean exactly middle gray. Meters work at 14%, not at 18%, which is about 1/2 stop.
An incident meter (handheld at the subjects location, in the same light) will simply just read the actual light level, and then it is very likely that the white dress will come out white and the black dress will come out black. This is wonderful in the studio, but a bit of trouble in the outdoors.