I don't use Cpanel because my host has it's own web interface, but I'm assuming you could have all your email forwarded to Outlook or another email application. Then, set that email program up to check email every 5 minutes, or however often you want it to check. Then, while you're online, keep your email client open and it should notify you when you have new email.
That's how I'd do it, at least. I don't know how Cpanel would be able to notify you, because it exists on your Host's server. My brother programs for a large online website, and he gets text messages on his phone when systems go down, but I think that's something different and would either not be possible or very impractical ($$$) for your purposes.
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Rob Jenkins
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