Can metal oxides react with water to form a hydroxide, then that with HCl to make a salt?
tl;dr: Yes, depending on extent of reaction

The group 1 and (group 2) hydroxides for example: $\ce{NaOH,  KOH, RbOH, CsOH, Ba(OH)2, Ca(OH)2}$ are strong bases, being essentially fully ionized in aqueous solution; (although some are weaker $\ce{LiOH}$, $\ce{Mg(OH)2}$) . These should react with $\ce{HCl}$ - a strong acid forming water and a neutralisation product a typical corresponding salt $\ce{MCl}$ or $\ce{MCl2}$ .

Being soluble in aqueous envronment implies the salt is also obtained in this phase, so the question will be on extration method to use, in order to get this salt product in solid form.

Why I said depending on extent of reaction, is beacuse some metal oxides e.g $\ce{MgO}$ hardly form the hydroxide in the first place, and also insolubility with render the second reaction effectively out of question.