Do individual (free) nucleotides base-pair with other free nucleotides?
The base-pairing in solution only provides 2-3 hydrogen bonds, which the nucleotides could also form with water itself. There are no stacking interactions between bases in water like in a DNA helix. So I strongly doubt that the nucleotides would form a significant amount of dimers in water.
I found a paper confirming my assumption:

Short nucleotide fragments such as mono- and dinucleotides are
generally unable to form stable hydrogen-bonded base pairs or duplexes
in water.
Minimal nucleotide duplex formation in water through enclathration in self-assembled hosts.

An easy way to confirm this would be to observe the proton NMR spectra of free nucleotides. Base-pairing in nucleic acids shows characteristic signals in the imino proton region (around 10-15 ppm), which are not visible in unpaired nucleobases due to chemical exchange.