They state in the user manual that you should not use the device with an internal tuner unless the SWR is below 2:1. If the unit is switched into the off position, would it be ok to use the internal tuner then to tune bands that are slightly higher that 2:1 SWR?
No.
If you have an external tuner, you can put it before the tuner so the tuner presents a good load to both the noise reduction unit and the radio. When your antenna tuner that is internal to the radio is tuning your antenna system, it doesn't change the SWR outside the radio. it adjusts the SWR inside the radio after the tuner.
It's not so much the tuning process that is the issue, it's the voltage extremes that are present in a high SWR circuit. When tuned, the voltages outside the radio are increased since the radio isn't limiting power.