ProcessMessages is intentionally not exposed because it seems most people who use it or want to use it fail to understand or account for the risk involved. Specifically, there's a problem with reentrancy that can lead to crashes or other undefined behavior.
For example, if the user clicks Next, and in your NextButtonClick handler you call ProcessMessages, the user can click Next again during that ProcessMessages call, resulting in a nested invocation of NextButtonClick. The wizard isn't built to expect that, and your [Code] probably isn't either.
If you really do think you need to process messages, then you need to be extra sure to disable access to the UI, e.g.:
WizardForm.Enabled := False;
WizardForm.Enabled := True;
(Substitute WizardForm with whatever form is currently active.)
My advice, though, is still "don't even try it".