Matched Filters for attenuation detection?
Your interpretation of the matched filter for radar seems almost right, just to be sure, let me reiterate a bit: Think of it this way: we're sending a pulse function $p(t)$. If a target in distance $d$ reflects the signal, we receive $\gamma \cdot p(t-\tau)$, where $\tau = 2d/c$ is the total travelled delay. 

The problem is: how to sample such a signal? Let's say your pulse was rectangular, you would need a lot more samples than the pulse width to know its extent and therefore, the proper delay. This is where the matched filter helps.

Applying matched filtering to your received signal, you filter it with $p(-t)$. This gives a signal comprised of the autocorrelation function $\varphi_p(t) = p(t) * p(-t)$, i.e., we obtain $\gamma \cdot \varphi_p(t-\tau)$, more or less. Now, the ACF always has its maximum at $t=0$, which greatly helps for the sampling. Also sampling the ACF at zero gives the optimal SNR: you gather the whole energy of the pulse into the sampling point. It's also called pulse compression for this reason.

Now, back to your question: You can extract both from the received signal, the delay $\tau$ and the reflection coefficient $\gamma$. In fact, this is often done. People call it RCS (radar cross section). Note that it is not so easy to infer material properties from $\gamma$ as $\gamma$ is typically highly direction dependent: the geometry of the object has a lot of effect on how strong the reflected wave is.