Hi,
You can but whether it is worth it remains to be seen, with the possible (there may be none) problems, caused by the upgrade. After all the laptop was first released nearly 12 years ago which in PC terms is a lifetime, (for Windows it is 4 OS versions ago). You may be better off just increasing the RAM and staying with WinXP, which you know at least works properly.
Dell does not support Win7 (not even Vista) for this laptop so there are no drivers available for it from Dell. It ''may'' be that the generic Win7 drivers that are installed, when you install Win7 may be good enough for all the laptop functions to work correctly, but this is not guaranteed. If not you could try downloading drivers from this link if some functions do not work properly. (http://www.driverscape.com/manufacturers/dell/laptops-desktops/latitude-d600/2170 as you can see there are not many available) or by going directly to the device manufacturer's website (e,g, Realtek for the audio drivers) for the drivers
With regard to RAM, here is a link to the User Guide, scroll to p.95 to see how to safely remove / install the memory modules (RAM) http://downloads.dell.com/Manuals/all-products/esuprt_laptop/esuprt_latitude_laptop/latitude-d600_user%27s%20guide_en-us.pdf You will need to install 2 x 1Gb PC2100 SODIMM (200 pin) memory modules.
Hopefully this is of some help.