It's not quite true to say that the receiving computer never sees the domain name. It always can see the requested domain, even if it ignores it. That's how multiple web sites with different domains can be hosted behind one IP address. The server, upon receiving an http connection, knows which site to respond with because of the domain given in the request.
As for using only one A record, I think it's better to use several. The company may be using only one server right now, but it might use many in the future. Best to set up mail and ftp and so on, for that future eventuality that it goes to a different server with a different IP address.
-------------------------------------
• Every joy is beyond all others. The fruit we are eating is always the best fruit of all.
• It is waking that understands sleep and not sleep that understands waking. There is an ignorance of evil that comes from being young: there is a darker ignorance that comes from doing it, as men by sleeping lose the k