Hydrohalogenation vs Hydration of Alkenes
"I'm thinking that, because the HCl dissociates to form hydronium ions and chloride ions, there are more hydronium ions than HCl molecules and therefore, hydration is likely to take precedence."

Definitely don't go by the that logic. The first step of hydrohalogenation requires the dissociation of $HCl$ and produce $H^+$ (/hydronium), so that the $H^+$ can activate the alkene forming the carbocation intermediate. This is also the first step of the competing hydration mechanism, as you ended up realizing.

The key here is the second step, where a nucleophile attacks the carbocation to form the neutral product. The nucleophilicity of water and chloride aren't extremely different. One might argue that "in a vacuum", chloride is a better nucleophile due to the charge (though that charge is quite stabilized over a large volume). But, practically speaking, water tends to attack instead of chloride in most situations. This is because when both are present, water tends to be in much higher concentration which increases the rate of the water attack pathway.

So consider your conditions, and if water is in much higher concentration than chloride, I would assume the hydration pathway will dominate.