I have a HP Laptop with a 64 bit Window 7 Home system.

Windows update keeps sending me 32 bit updates--should I down load these updates or just update 64 bit components when they are offered?

Assuming that it is proposing 32 bit updates, they are not applicable on your OS and the update packages won't be installed. You can give a try and see.

Hi,

Does the Windows 7 successfully download and install 32 bit update?

In general, Windows Update push is corresponding to the OS version. I recommend you to open the System Information and confirm the system type:
Run msinfo32 and press enter, System summary system type.

Best Regards,
Eve Wang