Yes, as long as it is free non-copy protected app, you can back up the APK file, then save it to a portable media OR upload it to Dropbox OR email it to yourself. Astro File Manager is the easiest way to back up and zip files.

Actually I have a "dirty trick" to confess. There is a way to access the market with the free emulator available from google, if you do a little tweak to add an HTC Dev Phone image to it (the image is publically available from HTC's website). It's a little bit complicated, but it can be done. You use the emulator to make a OS 1.6 virtual phone, but don't run it. Then, you drop the img file of the Dev Phone into the folder with the new virtual phone's files. Then start the emulator, open the virtual phone, put in a gmail address, and you have access. I'm a bit nervous about providing more detail should any powers that be cry foul, but there is blogspot post out there on the web with details.