Yes, in rotation — spinach is nutritious but contains oxalates that bind calcium, which matters especially for egg-laying hens.
What it means for conures
There's nothing specific to a conure that changes the verdict on spinach — it's treated the same as for parrots generally. A conure can handle a moderate portion.
The full picture on spinach
Spinach is rich in vitamins A and K, but its oxalic acid binds dietary calcium and can reduce absorption. For most pet parrots an occasional leaf is harmless; for laying hens and birds with calcium issues, frequent spinach is a real concern.
Offer a leaf or two, once or twice a week, washed well.
Rotate with low-oxalate greens like kale and bok choy.
Limit further for laying hens or birds on calcium supplements.