If you are using flat pedal then maybe you can get away with 1 shoe for both, but if you're on clip-in pedals I dont think you can use an spd shoe for running, spd shoes have hard soles not ideal for running not to mention that the cleats is slippery on rocky trail.
SPD shoes, even with recessed cleats has a stiff midsole. Although there are SPD shoes that look like sneakers (i owned about 3 of these already), you can't even walk on them for more than a kilometer without changing the way you walk. Hit a protruding stone and the cleat will slip.
If you'll go platform, you'll lose the clipped in benefit, but....there's always the option for clips or toe straps that fixie riders are using today. With this, you can use your running shoes on the bike event.