Best answer by Dave Olson
apt-get just uses normal routing to get to the server(s) listed in sources.list.
If you are using management vrf, that should "just work" if you login over the network, because we set up mgmt vrf routing by default when mgmt vrf is enabled.
You can also set up proxies for apt, but they aren't usually needed, unless your company has firewall rules, and has you using proxies.
If the hostname resolution was the only thing failing, and the change to resolv.conf fixed that for you, are there remaining problems?