Can we band pass filter QPSK signal?
Yes, you can bandpass the QPSK signal before matched filtering and demodulation if you wish to do so, but what you need to devote some thought to is whether such an action is a wise decision. The answer might depend on various parameters that you have left unspecified.


Bandwidth of bandpass filter $&lt;$ QPSK signal bandwidthIn this case, the filtered QPSK signal now has intersymbol interference (ISI) in it whereas the incoming signal did not, which makes the subsequent matched filtering and demodulation more problematical. Equalization might be needed to ameliorate the ISI which will add to the cost/weight/power consumption of the receiver, and error probability will likely suffer.
I didn't bring up the issue of the center frequency of the bandpass filter in the previous paragraph, but if the center frequency is different from the carrier frequency, then there is a whole 'other can of worms that you will have opened up.
Bandwidth of bandpass filter $&gt;$ QPSK signal bandwidthThis is a much better notion that the previous one. The issue of mismatch between center frequency of the filter and the carrier frequency is still there, though. But, is this a good idea? Maybe, maybe not. Remember that the matched filter is also a bandpass filter. Indeed, as pointed out here, the matched filter has transfer function $S^*(f)$ where $S(f)$ is the Fourier transform of the QPSK signal, and so the matched filter has large gain at frequencies where the signal is strong and low gain at frequencies where the signal is weak   -- a resume'-writer, no less, since it is emphasizing the strong points and playing down the weak ones. Thus, additional bandpass filtering ahead of the matched filter is not really necessary from a purely DSP perspective. However, your circuit designer colleagues might well insist on the extra bandpass filtering on the grounds that it helps with dynamic range issues in low SNR situations. 


So, explore all the ramifications before jumping into bandpass filtering. Do you really need to use a bandpass filter, or can you get by without it?