Well, not being a physics major, my assumption is that EM energy coming in the IR wavelengths works the same way as ER in the "visible light" wavelengths when they come through lenses. In other words, if you're looking at actual light coming from the physical object, even if that light is manipulated, then yes you can still see thermo just like you can still see red or blue even when the light is being warped.
On the other hand, if what you're looking at is a display screen that is rendering an image gathered by an electronic sensor, then it should be obvious that no, your natural senses are not in play. You can't see the IR signature of someone on on a CCTV image being shown in the security station, right? Exact same principle when you look through an electronic device that simply happens to be held close to your eye.
OTOH, just because binoculars say they come in vislight-blocking models AND vislight-compatible models and no other optical devices do, it doesn't mean that only binoculars are available in optical/lensed models. It makes perfect sense to me to assume that since goggles don't say they come in both, then the version they "should" come in is optical. If we presume that the goggles are bricked or powered off, should they be transparent and still see-through or are they now a blindfold since there's no image being generated? I assume goggles can be seen through by default, and therefore that includes thermographic vision if you have it.
The sorts of things where your natural senses are not relevant are cases like looking at a sensor feed, being jumped into a drone, and so on. I would assume that unless the device specifies it is NOT optical in nature, you can see though it naturally. Note however that many real life and futuristic/cyberpunky vision goggles should not be considered "see through" and are putting a computer generated image in front of your eyes, rather than directing EM energy that's literally coming from the objects you're looking at.
TL;DR: something like this you can either obviously see through, or should presume you can see through:

OTOH something like this, clearly your natural thermo is useless:
