Not really. Paradox of tolerance means not tolerating intolerance. The word “inherent” makes it wrong, though. There’s nothing inherent about conservatism that is anti-democratic.
The Paradox of tolerance only endorses the right of being intolerant towards intolerance; it in no way suggests that it's always a good idea to practice such intolerance. On the contrary, the actual "paradoxical" idea is that some limited tolerance should be extended even to the intolerant to the extent practical, since this helps promote the norm of tolerance in the first place even when intolerant ideas might otherwise appear to be prevalent. IOW, Popper's position is, to a limited extent, consistent with the one most clearly phrased by Thomas Jefferson: "let [the intolerant] stand undisturbed as monuments of the safety with which error of opinion may be tolerated where reason is left free to combat it."
People keep parroting this term, but I don't know if they have actually read the quote on Wikipedia.
In this formulation, I do not imply, for instance, that we should always suppress the utterance of intolerant philosophies; as long as we can counter them by rational argument and keep them in check by public opinion, suppression would certainly be most unwise.