No, you have to use damage effects to deal damage to a unit.
However, you can combine the effect and triggers.
E.g. you make a dummy effect that deals like 1 damage without any additional effects.
Then, if you want to damage a unit, you can use "Catalog - Set Catalog Value" to change the damage this dummy effect deals.
And then you apply the effect to a unit with "Environment - Apply Effect to Unit from Unit/Player".
It's not as elegant as the WC3 trigger, but it works.
Yeah there are at least two ways of doing this in the galaxy editor.
The first way is environmental (I forget exactly what it's called). The environmental effect allows you to deal damage from one unit to another.
The second way is to modify unit property: life. Then specify life = current - damage. The problem with this second route is that it doesn't allow you to assign kills directly. I'm sure less roundabout solutions will appear in the future (and maybe they already have).
Simply reducing the life will:
1) Not have any attribute bonus damage apply.
2) I think you'll have to account for shields yourself.
3) Will not provide the correct killer for "Unit dies" or "unit takes damage" events.
4) Will not have death types (like acid, fire, etc).