I would tend to say no.

Classical liberalism, in its original form, simply advocates for maximal individual liberty and minimal imposed authority. It doesn’t really stipulate any details - just that, when an issue arises that presents a choice between liberty and authority, liberty should be preferred.

Beyond that, democracy, in spite of its reputation, does not necessarily lead to liberty. If the majority votes to destroy the liberty of, or even simply kill outright, the minority, that would be democracy in action just as surely as any othe winning vote would be.

Lysander Spooner said it better than I ever could:

Majorities, as such, afford no guarantees for justice. They are men of the same nature as minorities. They have the same passions for fame, power, and money, as minorities; and are liable and likely to be equally — perhaps more than equally, because more boldly — rapacious, tyrannical and unprincipled, if intrusted with power. There is no more reason, then, why a man should either sustain, or submit to, the rule of the majority, than of a minority. Majorities and minorities cannot rightfully be taken at all into account in deciding questions of justice…

To say that majorities, as such, have a right to rule minorities, is equivalent to saying that minorities have, and ought to have, no rights, except such as majorities please to allow them.

Or as H.L. Mencken predictably put it much more simply:

Democracy is the bludgeoning of the people, by the people, for the people.