In a prerelease or booster draft tournament where each player starts with only 4 prize cards, will Iris add 20 damage even if no prizes have been taken?
No, it does not. Limited format tournaments may start out with fewer prizes than the standard six, but that does not mean those fewer prizes count as being taken.
Source: Plasma Blast FAQ (2013-08-15), TPCi Rules Team (2013-08-15)

Relevant cards

Note: All applicable cards may not be listed below.
BW10_101
BW10_81