No. The number of entrants that qualify for the Olympics doesn't change. For example, if the Olympics were next year, Canada would have three men and dance teams, two pairs, and one lady. The skaters who did the main competition and the team event would have to come from that. So, example, presume this is Canada's Olympic team.
Men: Chan, Reynolds, Rogozine
Pairs: Mt/M, D/R
Dance: V/M, W/P, G/P
One from each discipline would participate in the team event short program. Then Canada could substitute skaters in up to two disciplines for the free. IF a qualifying team DOESN'T have a participant in that event (lets say that the Canadian lady bombed at Worlds a la Chen Lu in 1997 and didn't qualify for the Olympics at Nebelhorn/whatever), they do get a slot for one skater, but the ISU wants the top skaters to compete.