While it's true that fossil fuels do provide an important role in variable management of the grid still, this is also accomplished with hydroelectric quite heavily in my area and over time the rates of each production method will adjust accordingly so I think it's still a reasonable assessment to look at overall production.
For example, during any period that the nuclear and hydro are running at capacity. If you reduced your constant power usage by 1kWh then during those peak periods, 1kWh less gas generation would be used by the network.
If your constant 1kWh of electricity would otherwise be exported to the US if you didn't use it, then it could be that 1kWh less coal generation would be used at some times.
Most people find it difficult to think about how their marginal increase in usage very often will cause extra CO2. Even writing this comment down has made me think about how CO2 production also depends on the future predictions of generators. It is complicated, but worth spending time to think about.
I think you are likely mistaken, although it is a surprisingly common misconception. Most places in the world, if you are using an extra kWh of power, the system needs to generate up to an extra marginal kWh from coal or gas.
Example 1: France generates power 70% from nuclear. However if a French person uses an extra kWh during base load, that could easily lead to one less kWh exported, which would most likely mean one extra kWh is generated from say coal somewhere else in Europe.
Example 2: New Zealand generates 60% of power from hydro. If I use an extra kWh of power at the moment (even at cheap rates), then if we have a drought in 6 months time, then an extra kWh needs to be generated from coal in 6 months time. I am presuming the coming critical storm[1] this weekend won’t fill our hydro lakes[2] and that the predicted long term dry weather pattern[0] will occur. I am a New Zealander.
You could be right if you are only using your power when it is cheapest (which usually implies the usage of base load nuclear), although it is surprisingly difficult to actually figure out whether you have generated zero extra carbon.
[0] https://www.rnz.co.nz/news/national/441393/hydro-power-more-...
[2] https://www.transpower.co.nz/system-operator/security-supply...
[1] https://www.newshub.co.nz/home/new-zealand/2021/05/rare-red-...
Edit: on second thoughts in NZ I am sure our lakes can’t fill that quickly from one good storm - the inflow rate is limited by the size of the river and the inflow rate is small compared to the storage size?