I think your question has nothing to do with "software", so I'll ignore this part, and only discuss the calibration part of it. Then again, your question is very broad and cannot be answered with yes or no: It really depends.
In some applications you might want to try to invert as much of the transfer function of your sensor as possible. In other applications you might not care about it that much and leave it in or only partially compensate it.
What's though true is that in general you cannot completely eliminate the effect of your sensing equipment. By the way it filters the "true" signal $x(t)$, some of its components might be filtered out and be lost completely. As a simple example: practically all real systems have some sort of low-pass characteristic so that very high frequency components will not do anything to it and thus never show up in $y(t)$. If you excite a 1 kHz low-pass system with a 1 GHz input signal, you cannot hope to get it back by inverting the low-pass characteristic, you'd have to divide by zero essentially.
There may be other reasons you would not want to compensate. Say your system does have a very small gain at some particular frequency. Then if you try to invert this behaviour, you'll need to amplify this particular frequency a lot. This would mean that any unwanted component, such as noise, would be strongly amplified at this particular spot. In applications like this you might want to do a partial calibration, where you do correct for the transfer function in a certain frequency region of interest only, and ignore the rest of it.