De-/protonation of R-OH group by acids and bases
Your first statement is correct. The basicity increases with $pK_a$, so a base with $pK_a &gt; 16$ will be able to deprotonate your alcohol.

Your second statement is also in principle correct; however, the value of the sum $pK_a+pK_b$ is solvent-dependent, and 14 is the value for water at standard conditions. $pK_a$ and $pK_b$ values of acids and bases depend on the solvent as well. For example, sodium amide is a strong base in liquid ammonia, but not so in water due to the leveling effect of the solvent. Dissolving sodium amide in water will give a solution of sodium hydroxide, which is not basic enough ($pK_a=13$) to deprotonate the alcohol.

Furthermore, the amount of deprotonated alcohol will depend on the difference between $pK_a$ values of alcohol and base, since the acid-base reaction is an equilibrium. For example, a base with $pK_a=33$ will deprotonate your alcohol to a greater extent than one with a $pK_a$ of 16.5 .