Can I do a starter with invert sugar if I add yeast nutrient?

I have invert sugar from sucrose and citric acid. No extra DME on hand, but I have some yeast nutrient. I have read that the lack of nutrients in sugar won't make a good starter (same that causes cidery flavors from fermenting with sugar), but will adding nutrient make up for this?

The problem isn't so much the lack of nutrients as it is the type of sugar. Yeast use different enzymes to digest different types of sugar. The reason you want to use DME to make a starter is so that the yeast are conditioned to digest maltose. If you make a starter with a different type of sugar then the yeast you produce aren't going to be used to digesting maltose and won't be making the proper enzymes in the quantity necessary to ferment your wort. It may still work, but you're starting your yeast out at a disadvantage and they will be stressed so you may get a slow or stuck ferment and/or have some off flavors produced.

So it sounds almost like no starter is better than a sugar starter.

Depending on the OG of your wort, you can get by just pitching a liquid yeast (as long as it's not a Wyeast Propagator) but you want to make sure you aerate really well since you are multiplying your yeast in your wort rather than in your starter. What gravity of wort are you planning on with this batch?

Getting info for a buddy. I think it's a little below 1.060 though. It's their first batch and they ordered a kit that comes with a standard white labs California.

I've pitched Wyeast activator packs directly in wort up to 1.070. I freely admit it's not the BEST thing, but it's worked fine and made great beer. Just aerate the crap outta the wort before you pitch to give it the best medium you can.