Amine Inversion and Paramagnetism
For somebody who is not well-versed in quantum mechanics, it might be natural to guess that this is the case. But if I were you, I wouldn't assume so.

Both electrons share the same p-orbital, and are therefore still paired. They both occupy the entire volume of the p-orbital. What they do not do, is to divide the p orbital up into two half-orbitals, with each electron taking one half.

There is a somewhat related question here, which might address some issues: How do Electrons Cross Nodes in Orbitals?