Hi there, @Gorhad! Thank you for providing these details.
If theres is a jumper cable needing to be installed, this means you have the Video Doorbell Wired model, as this is the only Doorbell that uses the jumper cable. By nature, the Video Doorbell Wired will disable your in home chime kit in order to power sufficiently.
In this case, and to answer your question, a Ring Chime would indeed be an excellent solution for alert sounds in your home.
If you do not have the Video Doorbell Wired model and feel like you have a different device, feel free to confirm what specific model and I’ll be happy to help further!