I would suggest an update, but I do not think that AA6 qualifies (need at least AA7). A big question is if it is a 32 or 64-bit system? For a 32-bit system there is some hope, though you may have to deal with some work arounds. Typically, AcroTray that automates the PDF creation may not work in Win7 (it does not for the AA5 I installed on Win7). If that is the case, you will have to change the printer port to file rather than Adobe PDF. Then you will be printing to file and have to open the file in Distiller to complete the conversion. You may be able to set up a watched folder in Distiller to automate the process a bit. Whatever you do, it will be trail and error and do expect some things to not work.
So the answer is to first install it and see if Acrobat runs at all and if the Adobe PDF printer is installed. If so, then try to print. If it locks up, then try printing to file and open the file in Distiller. If that works, then my suggestions may do the job for you. I was able to get AA5 to work on my 32-bit netbook with Win7 starter this way. Not that clean, but it works. I primarily did it as an experiment, but for you it is a bit more.
Unfortunately Acrobat 6.x is not compatible with Windows 7. Acrobat 9 and X are compatbile with Windows 7. As there was an upgrade path from Acrobat 6 -> Acrobat 9, you may want to try to buy an upgrade version of Acrobat 9 Professional. Adobe is no longer selling Acrobat 9 Professional, but a quick search of the internet reveals quite a few online retailers still selling it. That may be a more cost-effective solution for you to get a version of Acrobat that is compatible with Windows 7.
Hope this helps!