Is the visible light spectrum from "red-hot glass" at least close to Blackbody Radiation?

If you can see through it then it it is not black body radiation.

A blackbody emitter must absorb light of all wavelengths that is incident upon it and must be in thermal equilibrium. i.e. It must be "optically thick" at all wavelengths.

It may have a spectrum similar to the Planck function if the partial absorptivity is independent of wavelength. This is what LLlAMnYP is suggesting.

Edit: Please note important Caveat #2 at the bottom.

The Russian wikipedia page for Kirchhoff's law of thermal radiation is simpler and shorter than the English version, however it contains the answer to the question, which is absent in the English version. Translation follows:

Bodies, whose absorptivity is frequency-independent are called "gray bodies". Their emission spectrum is of the same form as a black-body spectrum.

Kirchhoff's law states:

$$ \frac{r(\omega,T)}{a(\omega,T)}=f(\omega,T) $$

where $a$ is the (temperature and frequency dependent) absorptivity of the object, $f$ is the black-body spectrum and $r$ is the emission spectrum of the object.

A high-quality sample of glass does not induce perceptible changes in color (well it does, and you can see this from a prism, but that's beside the point right now) so it may be safe to say, that in the visible part of the spectrum $a$ is constant. In that case, the emission spectrum of hot glass is

$$ r(\omega,T)=a(T) f(\omega,T) $$

i.e. proportional to the black-body spectrum (in visible frequencies, we aren't discussing any others right now) with a frequency-independent coefficient.

Caveat: room-temperature $a$ may be $\omega$-independent. High-temperature $a$ need not retain that property, though it might to some degree.

Caveat #2: human perception is a terrible way to judge the absorption spectrum of glass. A human is sensitive to the value $1 - a(\omega)$ and how uniform it is. A good glass is highly transparent and probably absorbs much less than it reflects (4% IIRC). But a human will not be able to distinguish between $a(700nm)\approx0.01$ and $a(400nm)\approx0.001$ (numbers taken of the top of my head). This will completely skew the thermal radiation spectrum.

EDIT: Here's some data on the complex refractive index of silica glass. See bottom of page 7. It appears, that the absorption of glass in the visible spectrum is indeed rather uniform. $k(400nm)=.7\cdot10^{-7};\,k(700nm)=1.1\cdot10^{-7}$, which is quite a bit more uniform than I initially expected. Thus the emission spectrum of glass compared to black-body is somewhat red-shifted, but not drastically.