First of all there is no such thing as the "You've met this perfect girl". I would council you to dispel such silly and outright dangerous notions.
As for your hypothesis, I would invest my time and money, if the risks were proportional to what I stood to gain.
Under this risk/reward assessment; crossing the seven oceans, spending untold money, risking a stray bullet from the American Maddow, all for one stranger of a woman is not proportional.
I was in this situation after her student exchange programme ended. The lame star crossed lovers whom will surmount all odds, soon turns into a logistical nightmare, every visit you will have to pay hundreds for a place to stay, travelling expenses, gifts for families etc.
The strange places and faces will quickly wear you out, if she does not first.
Are attractive, chaste, religious, maskeen girls whom are kind hearted in such a low supply in Saudi?
Be careful that you are not being mastered by the one eyed cyclops from your lower regions.