Are electrons just incompletely evaporated black holes?

Yes and no.

Electrons - and all other elementary particles - may be viewed as microstates of very tiny black holes. As one considers increasingly heavy elementary particles (e.g. those in the Hagedorn spectrum of string theory), they increasingly morph into black hole microstates. When the elementary particle masses sufficiently surpass the Planck scale, most of the elementary particles look like typical black hole microstates.

So quantum gravity as we understand it today implies that there is a gradual transition from elementary particles and black holes.

However, if the elementary particles - very light black hole microstates - are (much) lighter than the Planck scale, the description of these "black holes" using the most naive equations of general relativity (Einstein's equations) becomes highly inaccurate. Corrections such as (powers of curvature tensors) $R^n$ to the equations of motion, and various quantization rules and other deformations from quantum mechanics, restore their importance – those can only be neglected in the very large size limit.

Consequently, most predictions made by classical GR are seriously inaccurate or downright wrong for the elementary particles if they are treated as black holes. For example, the charge/mass ration of an electron (or other known charged particles) vastly exceeds the upper limit defining "extremal" black holes in GR. Such black holes wouldn't be classically allowed, but this regime is highly non-classical, so these objects do exist with the known properties.

It is actually necessary for the charged elementary particles to behave as "not allowed" overcharged superextremal black holes. It's needed for regular large charged black holes to fully evaporate, which is needed for other reasons. All these claims are equivalent to the so-called weak gravity conjecture.

http://arxiv.org/abs/hep-th/0601001

Classically, a spinning, charged black hole has constraints on its angular momentum and its charge in relation to its mass. Otherwise, there is no event horizon, and we have a naked singularity rather than a black hole. An electron violates both of these limits, so electrons definitely can't be black holes.

We could ask whether electrons are instead naked singularities. However, we don't observe that electrons have the properties predicted for these naked singularities. For example, the naked singularities would have closed timelike curves in the spacetime surrounding them, which would violate causality, but there is no evidence that electrons cause causality violation.

A separate issue is that in a scenario where these were originally black holes (presumably primordial ones), then I also don't think it's possible for them to evolve into naked singularities. This would violate what seems to be pretty solid support for cosmic censorship. But I suppose you could just postulate instead that there were primordial naked singularities.