The four point garbage matte doesn’t transfer over to After Effects. However, if you use the “Crop” effect in Premiere, After Effects will interpret the effect information as a layer mask.
As was mentioned earlier, once you have your footage cut together and masked in Premiere, you could export as a .mov using the animation codec with millions+ of colors, and this would at least keep the alpha channel information when you import that new piece of footage into After Effects.
Depending on what system you have, there are some hardware-enabled effects that work in both programs. For instance, I have a Matrox Axio LE system, and effects like the Matrox Chroma Key, and Matrox Blur/Soft Focus transfer back and forth. As a general rule, only effects that are listed in After Effects’ presets bin AND Premiere’s effects list are cross-software.