Just look at the dryer plug. If it has four blades, it has a neutral.
EDIT This is wrong, both the three prong and four prong have a neutral and are 120V/240V.
Another way is to put a ct on each conductor and run the dryer for a minute. If the two are different, there is a neutral.
But it may be fine to treat it as a 240 only appliance, depending on what you are trying to accomplish. If you want to identify every Watt consumed in your house, you need to capture the 120V component. If you are trying to arrive at a short-list of major consumers and subtract that from the whole to get an “everything-else” number, maybe you can treat the dryer as a 240V appliance.
Here’s a cycle of my dryer:
You can see that the whole thing sits on a base of about 200 Watts. That’s the 120V motor. I zoomed in on the motor during the cooldown cycle and got this:
Average 203W. So the whole drying cycle took about 51 minutes. Call it an hour. Total energy was 2.43 kWh. The motor ran the whole time at about 200 Watts. That’s 200 Wh. The 120V component is about 8% of the total.
So if I were to measure just one conductor, the result would be 8% high or 8% low depending on whether that conductor carries the 120 component. You can determine this by running for a minute with a CT on each. Assuming you measure the -8%, in this example you would see the dryer using 2.23 kWh and 0.2 kWh attributed to your “miscellaneous” category.