Don't take this as a definitive answer, but I have multi-aliased CentOS
boxen.
I find that outgoing connections always come from the main IP address,
not the aliases. In particular these boxen are web servers hosting
multiple sites, hence the multi-IP and connections to the database all
appear to be from the main IP.
Applications can be attached to individual IPs, but I think the default
routing is to use the main IP of the interface.
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