You'll have to write the code yourself because the function that sends out that particular emial is unlikely to have a plugin available to do what you want.
The easiest way would be to simply have wpmu send the emails to an email account dedicated to recieving those emails and just forward it to your phone.
EDIT:
btw, this is not the only method to send a text message to your phone. However, it is the only "free" method. In order to send an actual sms message to your phone you would have to have access to an SMS gateway on your particular phone network. The devices alone are expensive and you still have to pay 5 - 10 cents per message sent. Due to the costs, you typically only see companies like Google, Yahoo, etc install a gateway. However if you search around a bit i'm sure you could find a company that operates a gateway and provides access for a monthly fee(clickatell.com is one that comes to mind).
Also, try to avoid companies that offer software SMS Gateways because the so called "software" does the equivelant of sending an email to the network operated email gateway(which you could do for free).
And my final words are: Remember that you will still be charged standard text messaging rates no matter how the message is sent to your phone. So if you have 100 signups a day that's $10 USD a day (based on the standard 10 cents per message rate).