Depends on what you mean by "functionally expressed" and the promoter in question. There are examples of Saccharomyces promoters working very well in Pichia (see e.g. PMID 10806427 for the CUP promoter, I think the GAP promoter works as well but I can't recall where I get that from) but I doubt this can be generalized to every promoter.
Daer Alejandro, thanks for answering my question. I meant if Pichia is able to recognize a S. cerevisiae promoter and express the downstream gene. I would like to use GAP, since it is used widely in Pichia expression vectors, although blasting the promoters of the two spieces didn't give me results. If I could use this promoter I would gain a lot of time :D
The one used in the pGAP vectors from Invitrogen is from Pichia itself, not Saccharomyces. My recollection is that the GAP promoter from Saccharomyces also works in Pichia, but as I mentioned above, I can't remember where I got that from, so...