I want to see the perspective we get from an 10-20mm wide angle lens on a crop body DSLR.
Can a mobile phone camera be considered equivalent to 10-20mm wide lens on a crop body?
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Generally no. The camera on most cell phones provides a field of view equivalent to a 28mm lens on full frame, give or take. That's roughly like the field of view of the long end of 10-20mm on an APS-C camera (15-30mm-e, or a little narrower for Canon). But it doesn't give you a good sense of the wide end, which I assume is most interesting.
There are a few phones on the market with wider lenses, usually as an entirely second camera module — the LG VG35 ThinQ is one such current example. This has a roughly 16mm-equivalent lens.
If you're just trying to get an idea of what a wider field of view will look like, you might try supplemental lenses designed for smartphones. These are terrible in terms of quality so I don't generally recommend them, but they might get you what you want. These usually come in the form of "0.45×" converters — they'll make 28mm into about 13mm. So, if you're just trying to get an idea of what this field of view looks like, that might be a very cheap option.
If the smartphone you want to buy offers a field of view that is equivalent to that of a 15-32mm full frame lens, then: yes. As there are tens of thousands of different phones out there, we cannot say for sure if phone A or phone B offers a feature without doing the same research that you would have to do - over and over again, because phone C will most likely differ in relevant ways.
If you want to know about the average field of view of a smartphone, I recommend reading What is the focal length on your typical cell phone camera?. The answers also include the necessary equations of you want to do it on your own.