You can swap the engine with the transaxle still in place, but would be much harder than just removing it with the engine. Can be done, and you\'ll have just enough room. But you\'ll likely find that it was easier to pull it out than put it back together - clearance wise.
2002 Corolla S, Silverstream, 1.8L 1ZZ-FE (VVT-i)
2003 Matrix XRS, Cosmic Blue, 1.8L 2ZZ-GE (VVTL-i) - RIP
2009 Matrix XRS, Blue Streak, 2.4L 2AZ-FE (VVT-i)