No, people with asthma do not take to the army. The procedure is quite simple.
At the commission in the military registration and enlistment office, the conscript goes through all the doctors and when they ask him, and this is sure to be asked:

– Are there any health complaints?
– Do you suffer from chronic diseases?

There is nothing to hide, and therefore you need to answer honestly because there is nothing to let yourself or others down. Since everyone sleeps in the barracks at once, and asthmatic attacks occur at night, then you need to tell the truth and only the truth. And therefore, oddly enough, our army benefits most from not conscription. No one needs an extra headache. Moreover, our military. As they say – more expensive for yourself. I am not talking about physical activity and weather conditions in which an asthmatic conscript can get, as well as about the consequences that may take place. All this is not even necessary for our army. 

Further. After an asthmatic person of military age announces his illness at the commission, he will be told:

– This is not a diagnosis!

this is a typical phrase of doctors in the draft board, and therefore there is no need to be surprised and protest, but to ask:

– What is the diagnosis? – still needed. 

In return, you will be offered a referral to confirm your diagnosis. As a rule, this is a referral to the hospital at the place of residence. You will be told how long you must undergo tests. And they will immediately ask:

– What medications do you take?

When you declare with your focus to the hospital to look at the nurses and be seen, the doctors will have to bo all in the course and passing the tests will be a mere formality. Moreover, doctors will already provide information about the conscript at the place of request, i.e. to the military registration and enlistment office. The conscript is punished according to all the data, by standing on the register at the clinic, by the prescribed drugs, etc., although this does not play a special role if the asthma is real.
The tests are quite simple and routine, the nurses will explain everything.
After passing through everything, a special sheet with the results is issued and with it you already need to go to the military registration and enlistment office. There, as a rule, they will not even look at him because they will already be aware of everything. It is still better to make a scanned copy of the sheet.

I do not know of any cases in which an asthmatic was called.
Well, if your asthma is fake and you did not go to college, and your parents are not tax officials, then there is no need to mow figs, bring them down to the army …

Supplement:
From June 9, 2014, there was information about conscription into the army with bronchial asthma. In some sources claim the appeal solely on alternative military service. What this service is to me is still poorly understood, however, and how to determine the severity of asthma after which you cannot be called up for service at all. If an inductee has an aggravation wearing a seasonal hacker , how to be in this case?
I will follow the information …