Can I measure solids-not-fat using nutrition facts only?

Yes, you can add up everything in the nutrition facts, and it will be a reasonable approximation. Even if there is something in the milk which is not noted in the nutrition facts, the contribution to the total weight should be very low.

If you want to be very precise, you have to make sure that you are doing the right calculation. In your list of things to add, you didn't mention the carbohydrates - but they need to be included, and you have to decide how to count sugars, and besides, make sure that you are reading the label properly (are sugars and fibre included in the number of total carbohydrates or not)?

I said "if you want to be very precise", because it might well turn out that it is not needed. Using this kind of formula is a decent starting point, but not guaranteed to give you great ice cream. First, this kind of formula starts losing its predictive abilities when taken out of context, and the original context for ice cream formula are dairy ice creams. Second, stabilizers and emulsifiers will have a big effect on your texture, not only the ones you add yourself, but the ones already present in the almond milk. So, you will have to go through several iterations of tweaking anyway. Given that the almond milk is almost all water, you can just as well drop it from the calculation of the starting recipe and count it fully towards the water.

Fiber is often (usually?) skipped on nutrition facts, as it has zero nutritional value (even though it's quite helpful in the process of digestion), and is definitely a non-fat solid, so it may skew the numbers quite a bit in case of certain foods. I can't quite imagine fiber-rich ice cream though, so in your case you should be fine.