If you're on an AT&T unlimited plan and using a BlackBerry, you have BIS. AT&T's BlackBerry Data Plan
is a BIS data plan. They just don't call it BIS on their system or on your bill, and they don't charge extra for it either - never have (none of the big 4 U.S. carriers have). Look next to your network connection type symbol (the 3G, H+ or 4G depending on the OS version, or the Wi-Fi when connected), if you see that little 4-dot BB logo, you're BIS connected.
The pop3 accounts are going through and handled by the BIS. The BIS polls your account every 15 minutes. If something is there, it pushes it to your phone over the BIS connection. It will check again in 2 or 3 minutes and push those if something is there again, and check again in another 2 or 3 minutes. If you get a lot of emails, they will seem to be constantly streaming in. If during the following check, there is nothing there, then it goes back to 15 minutes - until something is there again. Other than a BES or BES Express setup, there is no other way to make it work in BBOS 7 and older - you have either BIS or BES, or you don't get any emails at all using the native device email client (I won't go into third party email clients than can use wi-fi like LogicMail). You can set up, or look at the account settings on your phone, or through the AT&T BIS portal on your computer using the web address:
https://bis.na.blackberry.com/html?brand=mycingular and using the same login info you use on the phone to get through the email setup.
My wife and I both have grandfathered unlimited plans, too, left over from when we both got Pearl 8100s back in '07. She switched to the iPhone 3G in '09 keeping the unlimited plan (now on an iPhone 4), and I upgraded to the 9800 in '10 keeping my unlimited BlackBerry plan. Still $30 each.
How BIS will work (or not work) in BB10 in the U.S. is not yet known, considering none of the big carriers ever passed the BIS fee on to their customers before. Apparently, the BB10 phone can handle pop3 accounts in-device now (the way iOS and Android have done it). That means that the device is now polling the pop3 email server instead of the BIS. That would mean more battery usage, even if just a little more. Whether that polling increases to every few minutes after getting an email still happens, we don't know. No one with a Z10 in the other threads about BIS have tested the pop3 handling - yet. But, the Z10s have BIS connection capability since almost every BB10 screen shot shown in the last few months had the BIS symbol.
On the positive side, AT&T has let people continue their unlimited data plans even when upgrading to a 4G LTE phone - so it shouldn't be any different for the BB10 phones. It's not as easy when going through a third party dealer online (like through Amazon) or in-person (like at Best-Buy), as they usually only have the currently offered plans available for you (or them) to click through - they can see you have an existing account to allow upgrade pricing, but apparently not what the existing plan is. But, going through the AT&T account site, you will have your existing plan showing, giving you the option to contiue it. That's what my wife did when getting her iPhone 4 just this past summer.