Paraformaldehyde is said to permeabilize the plasma membrane in many cases to some extent - since the nuclear envelope membrane has a different chemical compoisition (mainly in terms of cholesterol) I would not assume it does.

What does paraformaldehyde do to cells?

Paraformaldehyde causes covalent cross-links between molecules, effectively gluing them together into an insoluble meshwork. The reason cells must be fixed prior to immunostaining is quite simple. You need to permeabilize cells to allow antibodies to access intracellular structures.

What is used to permeabilize cells?

Permeabilization provides access to intracellular or intraorganellar antigens. Two general types of reagents are commonly used: organic solvents, such as methanol and acetone, and detergents such as saponin, Triton X-100 and Tween-20.