Should I filter before calculating power, if I'm looking for relative changes in power? I am building a "scanner" sort of program, which reads IQ samples from an rtl-sdr stick, and keeps track of the power on certain frequencies, in certain bands.  I am interested in detecting activity on frequencies, which I do by looking at changes in power.  Since I'm simply calculating changes over time, can I get away with not filtering the data before calculating power, or is there some reason I should filter?
If the output from the SDR matches the band you're interested in, I see no point in filtering.

You want to filter when you have a scenario similar to this: you want to track the power in a band of $B$ Hz around a frequency $f_c$, but the SDR's output covers a band that is larger than $B$. In this case you want to filter, since otherwise a signal outside the band of interest could affect your calculations.