If I use Caterpie's "Pupate" Poke-POWER to successfully evolve into Metapod, can I then immediately use Metapod's "Emerge" Poke-POWER to attempt to evolve into Butterfree, all on the same turn?
Yes, you can.
Source: PUI Rules Team (2008-02-21)

Relevant cards

Note: All applicable cards may not be listed below.
SM10_2
SM10_2
SM10_3
SM10_3