It's kind of a loaded question James, yes it will spread or can spread. If you have not QT'd ALL of your display tanks fish, then even if you QT a fish for 6 months and add him in the display, he can still stress and get crypto. Crypto can be present / dormant in healthy systems and once you add a stressed fish, it can rear its ugly head. So the question boils down to your patience and willingness to eradicate the problem, or just keep it in check.
Eradicate would require display tank going fallow and all fish going through QT treatment, for roughly 28+ days, I have read numerous arguments on the actual time frame, but 4-6 weeks seems to have proven success. If you just want to keep it in check, you can treat your QT fish for flukes, Ich (crypto), worms, etc. over a few weeks and get them trained on prepared foods and try and get them very healthy before adding them to the display. There is obviously more to QT than first meets the eye, several things to consider.
I am currently running a 40g breeder with hyposalinity and treating with a combo of metro / prazi. I have a decent size sponge filter that i cycled prior to filling up the QT in my display sump. I use a strong powerhead instead of an airstone and I also have an old hang on skimmer from a nano system I used to run. I use it for skimming, but more importantly for bringing up oxygen levels. Running hyposalinity will help with the oxygen rich water and from what I have read, helps reduce stress by allowing the fish to use less energy on filtering saltwater and using the energy for its own immune system, to help battle diseases and parasites. If you research Hypo, you will read about a million different theories, especially on the exact salinity. Seems it has a pretty large variance for success and from what I read, it also seems to increase the success rate of medicinal treatments.
I highly recommend Googling up some proven techniques for QT's and then weigh the options and see which works best for you. One thing I recently learned is that trace amounts of Nitrites wont effect saltwater fish, as I stressed out that I had zero ammonia and 5 ppm nitrite and no matter how many water changes I did, I could not get the number lower and then I read a report from Randy Holmes-Farley and realized I didn't need to stress

QT's can be stressful, you end up putting a fish in a tank with virtually no structure, even with large PVC pieces. The fish look miserable and you sit there daily wanting to move them over lol. Just have to remain patient!!!
I've been keeping fish for a long time and this is my first QT tank, I used to be one of those guys who just tried to keep the fish healthy and eating, to keep ich at bay, but I felt it was time I start doing things right and so far I feel pretty good about my set up. I have had a few fish come through my QT and so far no diseases or deaths! Well, I take that back.... I tried to run cupramine before switching to hypo with metro / prazi, and followed directions to a T, I lost a Kole tang on the second dosage (48 hours into treatment) and immediately gave up on copper, as much negative as I have read on copper, I will not be using it anymore.
Anyways, I tried to spam in as much as I could without getting too long winded lol. Hope some of it helps anyways... let us know how you set it up and your experience with it.