It can in the written (classical) language and in the Western dialect, not so much in the modern Eastern dialect. The only place you find an 'f' in modern Eastern Assyrian is in loanwords.
This sound usually comes up just as a regular 'p', but sometimes it's a 'w':
nafsha -> nawsha (ܢܦܫܐ, "soul", like Arabic nafs)
nifTa -> niwTa (ܢܦܛܐ, "oil", like Arabic nafT)
banafsha -> banawsha (ܒܢܦܫܐ, "violet", like Arabic banafsaj)