I think it would be the opposite effect actually. Sleeping less, according to the article, seems to increase inflammatory and immune system responses, which are what cause allergies. So sleeping more, presumably, may decrease a person's allergic reactions.
Of course, this whole article is based on a really small sample size...I would take it more as a suggestion than a solid scientific result.
Sleep deprivation increase the levels of cortisol which is in part why you tend to put on weight when not sleeping enough. Cortisol is an anti-inflammatory.
I wouldn't be surprised if chronic lack of sleep increase inflammatory, due to some other mechanism, but for sure, short bouts of sleep deprivation has worked wonder for me to stop allergic reactions (I'm talking sleeping less than 4 hours/24 hours period - I usually need between 7 and 9 hours).
Of course, this whole article is based on a really small sample size...I would take it more as a suggestion than a solid scientific result.