human PGK1 promoter will initial human protein well. If you want to express human protein in mouse cells, you need to check weather this native protein expressed in mouse cells first. 

Dear Florian.

Every promoter including at least two elements. One of them is the core promoter elements such as TATA box located 28 bp upstream of transcription start site. Also your promoter may have CAT box and GC box. You can analysis your promoter sequence by a free software such as Eukaryotic Promoter Database or copy and paste your promoter sequence in a free software like Ape and check for these sequences. TATAAAT, also you may have more A between two T. CCAAT is a sequence of CAT box. Anyway, this elements have frequency. So if you have these elements, it means that your promoter works in all Eukaryotic cell lines. Because these elements are conserved during development.

The short answer is yes, especially if doing a transient transfection.  if you wish to make stable lines, expression will in part be determined by the integration site and copy number.