no.
once your pagefile is defragmented, a separate partition on your hardrive is almost redundant, since the pagefile is a container file.
there is (according to Microsoft), a bench markable improvement in pagefile performance if you move the pf to a faster less used hardrive, but this is definitely not going to be a practical noticeable difference to the vast majority of users
so, if you move the pf to a faster , less used hardrive, you might see better performance, but even this best case scenario perfomance boost is not likely to be noticeable or even measureable for most users
in most users situations, the amount of paging actually done is probably not much at all... this is almost definitely not worth the overhead for most of us