Can I get VP for special objectives (artifact and Voice of the council) when I dont control all planets in my home system?

With the basic, core rules, yes; the only points you cannot score are Secret and Public objectives.

However, most people I know play with the official Homeworlds variant (which can be found in the Support tab of the TI3 page on this site), which basically says you cannot score ANY points without controlling all the planets in your home system.

In such cases, I would say you don't score the points when you don't have your planets, but as soon as you reclaim your planets you would immediately gain the points for any Special Objectives you have that you didn't get points for.

Cheers sigmazero13