Keep in mind that as long as UART is sending the characters, A/D will not work even if you are using the Hserout command.

To be sure that your converter is started at predetermined intervals, I guess the best approach would be Darrel Taylor's Instant Interrupts. That way you would be able to send one character, start A/D, send another character, if A/D is finished then Interrupt will make a notice to your code, etc.

Ioannis