Yes, if you uninstall the version you have, and install a newer version, it should be able to pick up where the older one left off. Just don't have more than one version of certbot installed at once, as that can get it confused pretty good.
If snap doesn't work for you, you might try the pip instructions instead; sometimes (I think often) that's easier to install.
But upgrading certbot, as good idea as it is, really won't help you if your problem is connectivity to Let's Encrypt's servers.