STOP just unscheduled it, and CONT puts in back in the schedule list. So the process itself is unaffected. It can't avoid the STOP signal.
However, the world has moved on in the meantime. If the process was taking periodic snapshots of something (like CPU stats) those have been missed forever. If it was reading a pipe, the writing process would have got suspended when the pipe filled, but it may have timed itself out. So the answer depends on what the process should have been doing while it was stopped.
If the data is coming from a separate process that can buffer it until requested, and buffer overflow is avoided, then the data can be collected, but the appropriate time labelling depends on which process appends the time information.