This is a bit of a question mark. If it is a very old meter and manually read, it probably counts the NET consumption pretty well.
Most old mechanical power meters with the spinning metal disk do actually spin backwards when power is exported. When home PV solar first started getting popular, it was common to see people bragging about their meter going backwards and getting negative electric "bills". They had to modify the design of those meters to make them only turn forwards. One "fix" was basically a ratchet type mechanism that would just not turn backwards, so you would not get credit for back fed power, as it just could not go that way. They would then add a second power meter that would measure the power from the solar power system, or the grid back fed power. This way they could see the amount being fed back as a separate reading. Making it spin forward with exported power was more difficult for the mechanical meters. It is basically a motor with voltage feeding the field and current feeding the armature. Back fed power is just like reversing the polarity on a DC motor. This is also how low power factor loads turn the meter slower reading the real watts and not the VA multiple of amps x volts.
Some mechanical meters added some basic electronics to count the energy used so that it could be remotely read. But this caused a different problem. (a problem for you, not the electric company) All they did was count the rotations of the disk. Probably a magnet on the disk and a simple reed switch that just outputs a pulse each time the magnet passes the reed switch. That has no way of knowing which way the disk is spinning. And it will cause the electronic count to always go up, no mater if the power is flowing in or out. Now let's say you perfectly size a grid tied PV solar power system to net out ZERO!! During the day with the sun shining, the disk is spinning backwards. The system exports "let's just say 10 KWHs" and the mechanical dials on the meter counted down 10 before the sun goes down. Then the house loads consume that 10 KWHs again all night. The disk turns forward and the dials end up back in the same place, showing no power consumption. BUT..... The pulses counted by the remote read electronics counted 20 KWHs of the magnet passing the reed switch. When I still had a mechanical meter, they would remote read it, but still send out a person for a local read about once or twice a year. If the remote read number and the physical count on the dials are way off, that is a big red flag that something is wrong.
All power meters with a digital display in them can properly count imported and exported power. But if you do not have a Net Energy agreement, they will likely add the import and export numbers together an you will pay for your export. That is your fault for not getting "permission to operate" for a grid tied generating system.
I am all in on sticking it to the electric company, but when you start truly exporting power out to the grid, there are rules that need to be properly followed. If you are not going to get "permission to operate" for energy export, you MUST ensure your system will never export power. Many newer grid tie inverter systems offer a "Zero Export" option with CTs back at the grid connection. And a lot of cheaper "hybrid" inverters can only output power to the output side, and will not push power to the grid side. That type of system can probably be run without permission without ever being noticed by the electric company. And if you truly don't ever export power, I see nothing wrong with that. But if the system does export a little, you might end up paying for power you are giving away. That is the price you pay for not going through the connection process. I may have taken that risk if I had known up front how much my rates were going up as a "Solar Customer" with So Cal Edison. Every KWH I have to buy from them is costing me double what it did before I was a solar customer. It is a crappy deal to get hit with that to be "legal". If you install just a small system to offset only part of your consumption, it is very possible to end up paying the electric utilty more, even if you use less power because of the higher solar customer rates.