It does pretty much what it says - it filters the mains signal chopping out high frequencies. There's no (or not much) charge store so it won't help you in a brown out where the line voltage dips.
You could fit a battery-backed Uninterruptible Power Supply (UPS) but a good spec one will be expensive, CRTs aren't overly nice things to run on UPSes and you have to mess about with battery conditioning from time to time.
I wouldn't bother - I can't see that occasional brown outs will harm anything.
The US went through a period of being overly concerned about EMI and RFI (electromagnetic interference and radio frequency interference) so the FCC came up with overbearing rules about EMI/RFI filtering. That's why loads of Atari games have the filterboards that just sit after the edge connector and have a bunch of ferrite chokes on the lines and why you can remove them with no ill effect. Or why early US consoles had solid metal cases underneath the plastic with a few tiny holes for the cables. Eventually they chilled out a bit which led to the thin flexible metal cases covering bits of the motherboards.
The interface board on Star Wars PCB sets is a good example.
It just takes the board connectors, filters them, introduces another opportunity for poor connections, and then presents them at the top. Look at all that metal!