As long as you are using a single core to do both operations, it should be fine. Not quite sure if your ADC DMAs the converted value to memory directly. In that case, consult the datasheet. What exactly is your PIC part number?
May be, an algorithmic representation of your what and how you're doing would help getting better answers, I guess.
If I read it correct, you are:
1. Reading from the ADC and storing in a memory location
2. Sending the value via UART
3. In the meantime, if your ADC gives another value - store it at an alternative location and move it via UART.
4. This switching happens between both locations.
Assuming your ADC conversion rate is less than your UART transmit rate, you might not need to worry much. If your UART transmit rate is less than ADC conversion rate, then you have to either:
* Reduce the ADC sampling rate (or)
* Increase the baud rate of UART