If filter cutoff is 10 Khz then yes, BW at 1 Mhz goes away.
What is the filter cutoff you want ? 10 Kz or 1 Mhz ?
So you have to attack the source of the noise (which one would do concurrently) first
and then decide what compromises you can live with in the BW of interest. Keep in mind
filters , depending on design,. have group delay, eg. latency, as another issue and depending
on architecture/design have overshoot (eg. transient response gremlins).
Tradeoffs, always tradeoffs.......
Regards, Dana,.