Yea, it's possible and it's 100% possible to do it at home.
Being natural doesn't mean your hair no longer can BE straight - it just means that you've got to be ready to put in the effort to get it there.
I'm a curly girl (I don't know if that makes 4-a,b or c) - if I want to go straight I can just blow dry it out and then flat iron and follow up with a syran-rap wrap (if you have questions, check out macherieamour's website - she has a great tutorial).
And sometimes I do just blow it out (not to be bone-straight) and wear it like that. Big hair can be fun!
I think for natural ladies, the key factors are the TYPE of heat you use. I threw out my coil blow dryer and bought a T3 tourmaline blow dryer. I can blow dry my hair on the LOWEST heat level in the same amount of time it used to take me to blow dry my hair on the HIGHEST heat level with my old dryer. Less damage (but still damage), more ions...all that good stuff.
I also purchased a Chi ULTRA flat iron - not the standard black and red one but the tourmaline ceramic iron. I've also heard ladies rave about the FHI (I tried it, it worked fine) and Maxiglide (which did NOTHING for me).
When I'm blowdrying I spritz with Aphogee's Green Tea restructurizer as I attack each section (I do eight sections). Once dry, as I flat iron, I"m applying cones to each section. And right before I syran-rap my head, I spritz with the Green Tea again and wrap, and then bake that mess into my head with the hooded dryer.
I'm lusting after the BaByliss ceramic iron hooded dryer (about $99 on ebay) but haven't bought it yet.
Hope that helps.