Is it possible to apply a frequency filter a time domain signal?
When you want to explicitly apply a frequency domain operation on a given signal $x[n]$ then you need to obtain those frequency domain samples $X[k]$ of $x[n]$,

However, it's possible that you can also apply an equivalent operation on the time domain samples $x[n]$ which will implicitly realize the proposed frequency domain operation on $X[k]$ as a result. However in order to accomplish that, you shuld be able to convert the frequency domain operation into a time domain equivalent, usually by applying Fourier transform properties. 

If you cannot find such a (simple) time domain equivalent of frequency domain operation, then, no, you cannot apply it on time domain samples.  

As an example if you would multiply the DTFT $X(e^{j\omega})$ by a rectengular window of cotoff frequency $\omega_c$; $Y(e^{j \omega}) = W(e^{j \omega}) X(e^{j \omega})$ then you could also perform it on the time domain as a convolution: $y[n] = w[n] \star x[n]$ , but if you would do the following operation on the frequency samples $Y(e^{j \omega}) = log( |X(e^{j \omega})| )$ then it's hard to find an simple time domain equivalent case... 

(Note that I've used the theoretical DTFT, $X(e^{j\omega})$ to show the expressions while referring to the frequency samples which actually belong to DFT $X[k]$, please keep in mind the circularity issue when finding the exact expression.) 

For the mel-scale operations that are included in the box such as the $\log$ operation etc, the degree of nonlinearity will probably disallow an (simple) equivalent time domain expression to be formulated, and I don't know one such, but if you can find one, then why not.