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Technically yes, but in practice-probably not.
It is often said that purging 'doesn't work' in the sense that it doesn't "get rid of the calories" and create a deficit. This doesn't seem necessarily true.
The logical answer seems to be that if the food isn't fully digested before being purged, the calories aren't retained. This seems to be supported by this University of Pittsburgh study:
-"In 17 normal weight bulimic patients, there appeared to be a ceiling on the number of calories retained after vomiting. That is, whether or not bulimic patients had small (mean = 1,549 kcal, SD = 505) or large (mean = 3,530 kcal, SD = 438) binges, they retained similar amounts of kilocalories (mean = 1,128, SD = 497, versus mean = 1,209, SD = 574, respectively) after vomiting."
It is suggested that bulimics cannot completely empty their stomachs of the food, so some of it is absorbed, but it is true that some (perhaps most) of it is lost by the act of vomiting.
Whether this actually satiates you long enough to create a calorie deficit is a different question. Dehydration from vomiting and saliva overproduction as well as a suddenly empty stomach may mean you are hungry again unexpectedly quickly, and any calories lost by the act of purging would just be negated by the urge to replace those calories. Even if binging and purging was done repeatedly in a day, some calories are retained through each cycle so the TDEE could easily be met or surpassed.
Obviously the negative health effects of self inducing vomiting (markedly heart damage and raised cancer risk, lack of nutrient/vitamin absorption) far outweigh any possible benefit.