Relation between curve fitting and filtering
Generally speaking, I would not call a polynomial, in general,  a low-pass approximation to a signal. Per se, talking practically, standard definitions of the Fourier transform do not allow polynomials on $]-\infty,\infty[$ to have a useful spectrum. Generally speaking, polynomials (except constants) tend to infinity at fast rate, hence cannot be really limited in frequencies. 

So it is difficult to say a polynomial filters out certain frequencies. However, locally, on an interval, they can pass nicely through data points, so they can smooth data, to some extend. Typical examples are sensor trends or drifts, when they are monotonous, and peaks or bumps. 

You can find a lot of works on polynomial trend filtering, or polynomial peak filters. When the cost function for those fits is a squared error, you end up with a linear system in the polynomial coefficients, which turns into a weighted average of signal samples, that can be interpreted as coefficients of a linear filter. A famous example is the Savitsky-Golay filter, which was recently analyzed in frequency in 2011 by R. Shafer: What Is a Savitzky-Golay Filter?. This family of filters is also interesting as they provide smoothed derivatives.

But you can also fit a polynomial with other loss functions, like the $\ell_1$-norm, or with additional penalties. They are currently active topic in signal processing (I am working on some extension to Savitsky-Golay filters). Here are a few references, to start from:


On digital smoothing filters: A brief review of closed form solutions and two new filter approaches, 1986
Polynomial-Based Interpolation Filters---Part I: Filter Synthesis, 2007
$\ell_1$ Trend Filtering, 2009
Symmetrizing Smoothing Filters, 2013