Biodiversity is restricted by genome combinatorics?
Yes, we can say the number of species is limited as you conjecture.  However, quick estimation shows that the limitation has no apparent usefulness:

A reasonable estimate of the largest known genome is 150 GB (150,000,000,000 or 1.5e11 nucleobases).  The limit would be 4 raised to that power.  That limit is so high that it is too large for most calculators to calculate.  For instance. Wolframalpha.com fails to calculate 4 raised to 1e11, its maximum being about 4 raised to 1e9.  The result of 4 to the 1.0e9 power is about 1.0e602059991 or 10 raised to the 602059991'th power.

That rough result, 1.0e602059991, is so enormous that it is exponentially greater than the number of atoms in the universe (which is less than 1.0e100).  Hence, assuming the definition of species requires an organism to use at least one atom for its body, there is no consequence to saying the number of species must be less than this number.

The number of possible combinations of nucleotides is so outrageously large that it does not constrain the number of unique individual organisms or species.