Cascading conventional filter with matched filter The most upvoted answer to this question suggests to use a "conventional" filter in cascade with a matched filter to first remove out of band noise (with conventional filter) and then optimize signal to noise energy (with matched filter).

Given a sampled signal where it is known that all relevant signal information is located in signal's baseband such as this one (the relevant signal here has a gaussian shape):


and where additive noise information is not known (I know it is for that specific signal, but let's assume it could have any property (colored, white, correlated, etc)).

Is it always better to use the proposed cascaded filters (conventional and then matched filter) or would it be equivalent to only use a matched filter with a gaussian shape?
No, it is not “always” better. 

One would  prefilter in circumstances where it makes sense, like Eckart filtering where the signal is random and the background has a known fixed component.

Filtering, generally introduces correlation in a time series.  A simple matched filter is derived under the assumption of a white background noise. If the prefilter is a whitening filter, it is better but each situation requires its own analysis.

Food for thought, if both filters are LTI, a prefilter can be a post filter.