The short answer is yes. I have seen fogging from airport hand luggage x-ray machines after just 3 or 4 passes (this was using UK and USA not 3rd world airports!).
I use FP4 medium speed film (125 ISO) so it happens on this, not just high speed films as airport staff would have you believe. I used to work for Ilford Photo and ran the world-wide customer service area for product problems and saw lots of examples of airport x-ray fogging from around the world. The fogging I have seen on my film I know not to be an isolated incidence.
There are 4 ways around this that I use:
1. Have film delivered to my address at the destination I am travelling to (hotel or friends, etc.) by a supplier in that country.
2. Ask for hand search of film at airport hand luggage x-ray areas. You have a legal right to a hand search on film in the USA unless they are on red alert for terrorism. I have never been refused a hand search in the USA and I have had dozens of them at Newark, JFK, Boston, Chicago, Denver, Washington DC and San Francisco. I have also had hand searches of my film at Amsterdam, Berlin, Budapest, Geneva, Rome, Vienna, Hong Kong, Sydney, Auckland and Christchurch airports. I try and avoid flights in Europe, preferring to drive. This is specifically to avoid airport x-ray scans. If expecting a hand search of film I carry it in clear plastic bags (I use Ortlieb A3 map cases as they are large, very stong, have a velcro closure to secure the films inside and are crystal clear with a carry chord). At UK Airports you must ask for hand searches of film in advance and Manchester Airport has a policy of not doing hand searches so don’t bother asking here! If using Manchester I suggest using lead-lined bags (see below). I always travel to the airport for the flight leaving the UK by car or train, I don’t use UK connecting flights to limit the chance of film going through x-ray scanners.
3. Have film processed locally when on a trip. This can be done but is difficult as there are not many good b&w labs left.
There is an excellent lab in New York – Chelsea Photographic. They often turn jobs around the same day. If I’m in NYC I use them. Make sure you let them know to expect you and roughly how many films they will have to process. I have also used Reed Photo in Denver and Image Lab in Wellington, New Zealand. Mostly I bring exposed films back here for processing and endure the hand searches. In the UK for processing large batches of film I use Ilford Lab Direct. Up to 40 rolls, I process myself.
4. Use a lead-lined bag for transporting film – always carry in hand luggage though even with this. The ones I use are good quality and are made by Domke, available through Amazon. The large size takes 34 rolls of 120 film, medium bag takes 18 rolls of 120 and the small size takes 9 rolls of 120 film.