No, because natural selection is one of the subtractive processes that MUST reduce or eliminate a lot of that supply of variation in order to form a new species from some part of it. If you don't form species you may have lots of new variation, but then you aren't getting evolution. It's evolution I'm talking about, the formation of new species, which requires selection, which requires the loss of genetic material for unselected phenotypes.
It goes without saying that natural selection is a subtractive, but this process is ongoing, it does not stop when a new species forms. This is because the selective forces which first shaped this species are still acting on the individuals in the population. This is one reason why it is incorrect to suggest that you can’t form a new species, or even prevent evolution, if you have processes which can increase genetic variation.
To understand this think of a population which has adapted to exist within a stable ecosystem. In this case alleles that are positively selected, whether they come from the previous generation or are newly created by mutation, are those which allow an individual to successfully compete with others of its species. So in this scenario the increased diversity from mutation is offset by selection to maintain the expected phenotype of that species. To put it another way, evolution here acts as a conservative force, maintaining the species.
However, ecosystems do not remain stable and so the selective pressures on a species can change over time, and so alleles that were positively selected before may no longer be advantageous. This also means some alleles that were nearly neutral becoming positively selected for. If this is environmental change this could result in a shift in the phenotype of the population as a whole, meaning we would have to change the way we described that species. Or it may be a more limited change on the edge of a populations range, where the selective pressures vary from the pressures affecting the main population, so we define subpopulations.
Of course Founder effect is another example you highlighted, as would another example being mass extinction. In these cases the population may find itself in an environment where there is very little competition from other species, so more mutations may become positively selected as they allow individuals to exploit alternative niches instead of directly competing with the parent population, leading to diversification and speciation.