I'm pretty sure the answer to my question is "no," but I was hoping to be able to assign different ringtones to my work and personal email accounts, so that I'd know from the ringtone whether the email was work-related or personal.
At first glance, it looks like it should be possible, because when I go to "edit" a profile each of my email accounts are listed separately. However, if I go into one message account and change the ringtone, that same ringtone gets assigned to my other message accounts as well.
Unless I'm missing something, despite the fact that each account is listed separately, there doesn't appear to be a way to assign different ringtones to each account.
I wasn't able to accomplish what I wanted by editing an existing profile. However, once I created a brand new profile I was able to assign different ringers to different email accounts.