Judgment dragon vs Skill drain

Can Judgment Dragon activate its effect whill skill drain is activated?

Depends on the effect.

If you're referring to the effect that allows Judgment Dragon to summon itself to the field, yes, it can, and that effect won't be negated, since it activates from the hand.

If you're referring to the effect that allows Judgment Dragon to obliterate everything on the field except itself, yes, it can activate that as well, but Skill Drain will negate that effect. Despite this, you'll still have to pay the 1000 Life Points as cost.

^ima add to that. While Skill Drain is face-up on the field the effect that mills the top 4 cards of your deck to the graveyard is also negated but still activates.

the special summoning isnt an effect naito its a condition its not like edrags or mermails