The density of an aqueous solution
Answer to your question, "could the density of an aqueous solution be less than $\pu{1g/mL}$," is yes. See following examples:

The density of the commercially available 28% ammonia solution ($\ce{NH3}$ 1n $\ce{H2O}$) is listed as $\pu{0.9 g/mL}$ at 25 °C (Sigma-Aldrich Catalog).

MERCK Tabellen für das Labor has listed the density of 35% ammonia solution ($\pu{18 mol/L}$ concentration) as $\pu{0.88 g/mL}$ at 20 °C (Steffen's Chemistry Pages)

As obvious, the densities of various aqueous ethanol solutions are also equal to less than unity since the density of absolute ethanol is $\pu{0.789 g/mL}$ at 20 °C (Wikipedia). By a quick google search, I found the densities of various aqueous ethanol solutions listed in MERCK Tabellen für das Labor  in Steffen's Chemistry Pages, which is pretty interesting.