Only if the application source code fits the API of the library versions on your system. Otherwise you also need to port the application to your available library versions. Also using different dependency versions might surface bugs that you have to sort out yourself.

I only want to point this out because it often seems that the people that complain about flatpak do not grasp what maintaining a package entails, and your suggestion effectively puts you in the position of being a package maintaier for your specific distro. (But the upshot is that with open source software you are always free to do this, and also share it with other people through (community-) repositories)