Technically no - the 24hr "flexible booking policy" only applies to tickets purchased directly from United:
http://www.united.com/web/en-US/apps...romoCode=A5753
Terms and conditions- Applies to tickets booked at united.com or with United Reservations.
- The 24-hour timeframe begins at the time your ticket is purchased.
- Requests for refunds will be credited back in the original form of payment.
- Group tickets and tickets purchased using Western Union, cash or e-certificates are excluded.
- Reservations that are being held but have not yet been purchased are excluded.
- Any FareLockSM fees paid to hold a reservation will not be refunded.
It's possible that the website will not detect this and allow you to make the change, but I wouldn't guarantee it.