I too joined the FAA with childhood asthma and they made no mention of it - presumably the lung function tests were satisfactory.
Some years later on applying for a CAA Class 1 medical the consultant gave me a spirometer test (I'd never had one of those before, even in the Navy I'm sure) which was marginal, went out for some minutes and came back saying you can go home now, no Class 1 now or ever!
I appealed, cited my RN service but the "doctor" in charge of the CAA medical system was an ex-crab with a complete blockage on Asthma despite there being nothing in the book that specifically says it is a stopper. Absolute stonewall. I took some outside advice which showed the CAA had to reassess me if I wanted it (this was before I learned not to believe what the CAA tell you and check yourself), fittened up my pulmonary functions and reapplied to the CAA some months later. Results of tests fine. Results of examining doctor going to tell the Ch. Med pillock about it? A furious 10 minute shouting match that could be heard through half the building, followed by my examiner coming out looking ashen and saying he'd had to put his career on the line to persuade the geriatric old fart that he had no grounds to refuse my medical.
The CAA never mentioned the subject again.
Asthma can be a contentious thing, but as long as it was childhood asthma and your lung function tests are acceptable there should be no reason for it to be a stopper. Depending on the doctor involved, of course...