It makes no difference if the reader is in the base unit or not, they are all USB readers regardless.
If the reader is SD only then the updates won't help and it will never support SDHC and as heathfield says your only option is then to get another card reader (either an external one, or a replacement internal one)
If the reader is SDHC compatible then installing the updates should make it work with SDHC cards.
As we have no idea if the reader will support SDHC then the only option is to install the updates and see if that works.
(as a side note, if you've not got an update on your computer that was released in 2007 you will also be missing loads of important security updates on your computer, you really should be keeping your system up to date with it's windows updates)