Flat Spin
If it comes to it all it will involve is some paperwork unless of course you have got a criminal record.
Oh sure, it's not a terribly big deal but it's still a pain. I would imagine that it would be something the home country embassy would process at the same time as they process your visa.
As you say, the embassies are used to doing this for immigrant and non-immigrant visa already.
It's going to be an extra cost of course, and will probably deter those borderline wannabes from getting involved in flying, which is a bad thing. I suppose it might have a positive side to it for UK flying schools.
If you read the Act in full, the background check provision only lasts until the FAA comes up with some permanent security scheme for airports/flying schools. They have 12 months to do this. Security is quite frankly ridiculous, it's been simple to walk onto a ramp and steal a plane for ever.
I once managed to rent a plane three years ago in a small town in Tennessee without showing any ID or a pilots licence. I also paid in cash. If you think that's nuts, the person who checked me out (5 touch and goes was all it took) was the local deputy sheriff!!!!!
Absolutely Nuts