No, the interrupt occurring has no effect on the A/D. The A/D runs from the instruction clock or its own clock, depending on how you set it up. Both these keep going during a interrupt unless you deliberatly execute a SLEEP instruction to stop the processor clock.
At most, the 1 Hz interrupt could delay the interrupt routine processing the A/D conversion done, if you are doing this by using interrupts at all. There is no requirement that A/D results be handled by using interrupts. Even if so, the A/D will perform its conversion and write the result into ADRESH:ADRESL regardless of whether the processor is taking a interrupt or not. In fact, the processor itself is not really "in" a interrupt. That's only a software abstration. When the right conditions are met for a interrupt, the processor executes a call to location 4 and turns off the GIE bit in INTCON. That's all. The rest is up to firmware.
Once the A/D has finished a conversion, the result will be available in ADRESH:ADRESL. It is up to the firmware what to do with that. The value will stay there until a new conversion is completed. If the firmware doesn't start a new conversion until reading the result of the previous, then nothing can be lost. If a new conversion is started automatically, then it is possible for the previous data to be lost if the firmware didn't get around to reading ADRESH:ADRESL in time. Look at the acquisition and conversion time of the A/D and the instruction rate, and you will see there are generally plenty of instruction cycles to grab a conversion result, even if a new conversion is started automatically by the special event trigger of a CCP module. Just make sure the clock tick interrupt code is not so long that it takes longer than it takes the A/D to make a new result. This should be easy. Any lengthy processing is best handled by setting a flag and letting the foreground code get around to it when it gets around to it. The interrupt code should handle only the immediate servicing of the device.