Are you speaking about new generation of SSD that work like Sata-HD?
If yes, the answer to your ask is clearly Yes, out of the box!
The procedure is the same as any other disk.
Align to 32 bits?
This urban legend came from old BIOS who don't know other than HD, floppies, cdrom and so-called Zip-Drive. For booting on this kind of bios with USB devices (removable media bigger than 1,44MB or 2.88MB: Zip Drive geometry permits 100MB or 250MB), As
live USB has to be installed on
removable media, a nice script was built for reproduce the crappy geometry of a Zip-Drive.
Understandably, this caused some confusion because the first Live CD always used this script, forcing a bad geometry for the case when the USB key would be used on a very old bios. ( But in fact, this is not a Linux restriction: Other recent OS aren't even able to boot on such very old machines ;-)
Nothing to see with recent Linux using recent SSDs on recent BIOS.
I've personally purchased a 120GB SSD to put in an old laptop... The speed is wonderful!
Note: As Debian tries to stay essentially useful, minimal installation must be possible on very old systems (installation on a 486DX seems always possible, but I'm not sure... I can't do the test. but for the record, my personal web server runs in a VZ container powered by an old Dell laptop with a PIII Copermine @500MHz).