Yes, what counts for dpi is the number of pixels in the photo. If you stitch togther 4 images at 6 MP each, with (say) 1 MP of overlap each, you basically have a 20 MP image.
That said, yes you can print 12x36 -- it won't be 300 DPI (nor even 200 DPI), but it will still look just fine. Nobody looks at panoramas from 4 inches away -- they are, by definition, meant to be seen from farther away, to let you take it all in. 100 DPI is just fine.
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