Does Sparrow for iOS seamlessly integrate with Gmail's Send As feature?
Yes. Sparrow allows you to add "aliases" to each account so you can, from one account, send mail as a different user that's been registered as a send-as user in your Gmail account.

You click on the Preferences icon in the account view screen. Then click on the specific account. And then click on the 'Aliases' menu option to add new alises.

From one of my accounts I send mail as either me or my business account (which happens to be set at my business ISP to forward in to my Gmail account):



From the new mail composition window you click on the top bar to change who you're sending the email as and then you pick the account from the list Sparrow shows you:





It works the same way in Sparrow on OS X for what it's worth: