I run a Dell Inspiron 9300.
It had the 1.6 Ghz Pentium M stock processor, and I upgraded it myself to the 2.0 Ghz Pentium M.
I have not had any issues with WGA running on either processor, so I would venture to say your daughters machine should be fine.
The reports from Microsoft indicated that a very small percentage of the computers that had been flagged as invalid were actually inaccurate.
The bigger question mark seems to be the Office version of WGA currently being tested by a select group of people returning invalid data.
You might consider testing it before she goes off to college to verify that she won't have any issues.
I have spoken with a couple people who were running copies of Windows XP from a site license (and should not be), and they indicated that they received a message that they could not be validated for updates, but their computers still ran. I suggested that maybe they go to the local PC store and purchase a copy of Windows XP to solve the issue, to which I received a look like that was out of the question. I suppose it all depends on your priorities.
For my part, I have no issue with the WGA control being installed, it just takes an extra 30 seconds or so to scan the system.