Yes. Keeping 1 cartridge will help. And some beneficial bacteria will be living on your filter housing, some will be living on your substrate, any decorations etc. So you wont be starting over from scratch.
Going forward, getting rid of cartridges altogether would benefit you. A filter is just a box that contains media, and using proper biomedia and sponges that dont need replacing so often as cartridges would be the way to go everytime IMO
I dont think you have said what filter you have, but this video will show you in principal what im talking about.
Obviously, throwing the cartridges and replacing with proper biomedia will mean starting your cycle again, but short term pain for long term gain. If you dont want to go down this route though, in future 1 replacement cartridge at a time.