If I use Gladion can I choose Greedy Dice from my prizes and play it right then?
Greedy Dice can be played only if it's taken as a face-down Prize card. Gladion doesn't count as "taking a Prize card."
Source: TPCi Rules Team (2018-03-01)

Relevant cards

Note: All applicable cards may not be listed below.
SM4_109
SM4_95
XY11_102