Not quite, but almost. I've been using this setup for a few years now, with my own domain and Gmail.

To answer your questions:

- Login: You'll have two logins (Gmail address, GApps address you@yourdomain.com), but in daily use you only need the Gmail one.

- There is an additional copy of your emails in the GApps account. I configured GApps to move them to the trash after forwarding, but you can't outright delete them. I just empty that trash once a year. You'll also need to setup a mail rule that whitelists either all Spam, or (what I do) all your whitelisted addresses, so that no mails get stuck in GApps spam filtering.

- You'll be able to send emails in Gmail from your custom domain, and it will show only your custom domain in user-visible From: fields, if you configure Gmail to not use the Gmail SMTP user, but your GApps username and password. The "sent via Gmail" is what you get if you don't configure the SMTP server. FYI I use Server: smtp.gmail.com, User: me@mycustomdomain.com (this works!)

- You'll need to add the SPF and MX records for Google Mail to your DNS records. If in the future you ever want to switch from GApps to something else, you'll just need to change those and transfer your mails.

- I don't use any of the other GApps features, as to not get locked in.

If you like, I can send you an email so you can take a look at the headers yourself.

I have this setup. Your login remains the same i.e. gmail. For receiving emails it acts more or less like a forwarding service without an extra inbox. When you reply to an email sent to the alias, it will choose that alias to send from so you won't accidentally send from your gmail address. Also in email headers you'll see a gmail message id but it won't reveal your gmail address AFAICT.