Programming a Mini/Stamp using a Duemilanove

Hello. I'm developing an application which I'm prototyping on a Duemilanove, but the final version is going to run on a Mini or a Stamp. Since I'll only need to program the Mini/Stamp once, I want to save a few bucks by not buying an FTDI board.
So my theory is that if I remove the Atmega from the Duemilanove and wire power + RX/TX from Duemilanove breakout pins to the Mini/Stamp, I can use it to program the slave board through USB.
Is my assumption correct?

That should work. Don't forget to connect the grounds.