Where did you get your Windows 7 DVD?  The most probable reason you are not prompted for 32-bit or 64-bit is that OEM software does NOT have both on the disk.  Retail software does offer you the choice, but OEM does not.  Possible reasons Dell may have chosen to not offer 64-bit on the 200: If you do not have the hardware option I mentioned (if such a thing even exists - remember, that is just a guess) AND you have a Retail copy of Windows 7 that will allow you to choose 64-bit, there really isn't any reason why you couldn't install it ... Dell simply never supported it on the 200.
My Vostro 200 came w/a 32 bit version of Vista.  Technically, the machine should handle a 64 bit OS... even MS's upgrade tool says this.  Intel's web site says the Core 2 Duo has this capablility.  But when I upgraded to Win7 Professional using the custom option (completely wiping the disk), it didn't give me a 32 or 64 bit option.  It just installed the 32 bit version.  Is there some kind of 32 bit limitation imposed by Dell on this machine?  Did I forget to say the magic words?
Win7 Pro on 64bit Vostro = 32 Bit Version?